code stringlengths 114 1.05M | path stringlengths 3 312 | quality_prob float64 0.5 0.99 | learning_prob float64 0.2 1 | filename stringlengths 3 168 | kind stringclasses 1
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import sage.modules.free_module_element
from sage.misc.repr import repr_lincomb
import sage.structure.formal_sum as formal_sum
import sage.modular.hecke.all as hecke
import sage.misc.latex as latex
_print_mode = "manin"
def is_ModularSymbolsElement(x):
r"""
Return True if x is an element of a modular symbol... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/modular/modsym/element.py | 0.655667 | 0.466542 | element.py | pypi |
r"""
Local components of modular forms
If `f` is a (new, cuspidal, normalised) modular eigenform, then one can
associate to `f` an *automorphic representation* `\pi_f` of the group
`\operatorname{GL}_2(\mathbf{A})` (where `\mathbf{A}` is the adele ring of
`\QQ`). This object factors as a restricted tensor product of c... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/modular/local_comp/local_comp.py | 0.92627 | 0.776686 | local_comp.py | pypi |
from sage.modular.arithgroup.congroup_sl2z import is_SL2Z
from sage.modular.modform.constructor import EisensteinForms
from sage.modular.modform.eis_series import eisenstein_series_qexp
from sage.modular.modform.element import GradedModularFormElement
from sage.structure.element import ModuleElement
from sage.structu... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/modular/quasimodform/element.py | 0.877556 | 0.642713 | element.py | pypi |
from sage.structure.element import AlgebraElement
from sage.structure.richcmp import richcmp, rich_to_bool
from sage.categories.homset import End
import sage.arith.all as arith
from sage.rings.integer import Integer
from . import algebra
from . import morphism
def is_HeckeOperator(x):
r"""
Return True if... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/modular/hecke/hecke_operator.py | 0.785843 | 0.422624 | hecke_operator.py | pypi |
from . import morphism
class DegeneracyMap(morphism.HeckeModuleMorphism_matrix):
"""
A degeneracy map between Hecke modules of different levels.
EXAMPLES:
We construct a number of degeneracy maps::
sage: M = ModularSymbols(33)
sage: d = M.degeneracy_map(11)
sage: d
... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/modular/hecke/degenmap.py | 0.756447 | 0.507202 | degenmap.py | pypi |
import sage.rings.infinity
from sage.matrix.constructor import matrix
from sage.arith.functions import lcm
from sage.arith.misc import gcd
from sage.misc.latex import latex
from sage.matrix.matrix_space import MatrixSpace
from sage.rings.ring import CommutativeAlgebra
from sage.rings.integer_ring import ZZ
from sage.r... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/modular/hecke/algebra.py | 0.868813 | 0.521349 | algebra.py | pypi |
import sage.misc.misc as misc
from sage.modules.matrix_morphism import MatrixMorphism
from sage.categories.morphism import Morphism
# We also define other types of Hecke-module morphisms that aren't
# specified by a matrix. E.g., Hecke operators, or maybe morphisms on
# modular abelian varieties (which are specifie... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/modular/hecke/morphism.py | 0.783533 | 0.517144 | morphism.py | pypi |
from . import ambient
from .cuspidal_submodule import CuspidalSubmodule_R
from sage.rings.integer_ring import ZZ
from sage.misc.cachefunc import cached_method
class ModularFormsAmbient_R(ambient.ModularFormsAmbient):
def __init__(self, M, base_ring):
"""
Ambient space of modular forms over a ring ... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/modular/modform/ambient_R.py | 0.692122 | 0.354377 | ambient_R.py | pypi |
from sage.rings.fast_arith import prime_range
from sage.matrix.constructor import matrix
from sage.misc.verbose import verbose
from sage.misc.cachefunc import cached_method
from sage.misc.prandom import randint
from sage.modular.arithgroup.all import Gamma0
from sage.modular.modsy... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/modular/modform/numerical.py | 0.873754 | 0.561876 | numerical.py | pypi |
r"""
This module is now called ``ring.py`` (see :trac:`31559`). Do not import from here as
it will generate a deprecation warning.
TESTS::
sage: from sage.modular.modform.ring import find_generators
sage: find_generators(ModularFormsRing(1))
doctest:warning
...
DeprecationWarning: find_generators ... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/modular/modform/find_generators.py | 0.673192 | 0.490053 | find_generators.py | pypi |
from sage.rings.integer import Integer
from sage.structure.sage_object import SageObject
from sage.lfunctions.dokchitser import Dokchitser
from .l_series_gross_zagier_coeffs import gross_zagier_L_series
from sage.modular.dirichlet import kronecker_character
class GrossZagierLseries(SageObject):
def __init__(self... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/modular/modform/l_series_gross_zagier.py | 0.931719 | 0.574096 | l_series_gross_zagier.py | pypi |
from sage.rings.integer import Integer
from sage.rings.integer_ring import ZZ
from sage.rings.power_series_ring import PowerSeriesRing
from math import sqrt
def theta2_qexp(prec=10, var='q', K=ZZ, sparse=False):
r"""
Return the `q`-expansion of the series `\theta_2 = \sum_{n \text{ odd}} q^{n^2}`.
INPUT:... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/modular/modform/theta.py | 0.908346 | 0.690602 | theta.py | pypi |
r"""
Compute spaces of half-integral weight modular forms
Based on an algorithm in Basmaji's thesis.
AUTHORS:
- William Stein (2007-08)
"""
from sage.matrix.matrix_space import MatrixSpace
from sage.modular.dirichlet import DirichletGroup
from . import constructor
from .theta import theta2_qexp, theta_qexp
from c... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/modular/modform/half_integral.py | 0.916152 | 0.798187 | half_integral.py | pypi |
from random import shuffle
from sage.categories.graded_algebras import GradedAlgebras
from sage.misc.cachefunc import cached_method
from sage.misc.misc_c import prod
from sage.misc.superseded import deprecated_function_alias
from sage.misc.verbose import verbose
from sage.modular.arithgroup.all import Gamma0, is_Cong... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/modular/modform/ring.py | 0.804521 | 0.632077 | ring.py | pypi |
r"""
Weight 1 modular forms
This module contains routines for computing weight 1 modular forms, using
George Schaeffer's "Hecke stability" algorithm (detailed in [Sch2015]_). These
functions are mostly for internal use; a more convenient interface is offered
by the usual ModularForms and CuspForms constructors.
AUTHO... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/modular/modform/weight1.py | 0.870762 | 0.604574 | weight1.py | pypi |
from sage.matrix.constructor import matrix
from sage.modular.arithgroup.all import is_Gamma0
from sage.modular.cusps import Cusp
from sage.rings.infinity import infinity
from sage.rings.integer_ring import ZZ
from sage.rings.rational_field import QQ
from .finite_subgroup ... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/modular/abvar/cuspidal_subgroup.py | 0.489259 | 0.448245 | cuspidal_subgroup.py | pypi |
from sage.structure.sage_object import SageObject
from sage.rings.integer_ring import ZZ
from sage.rings.rational_field import QQ
from sage.rings.integer import Integer
from sage.rings.infinity import infinity
from sage.rings.cc import CC
from sage.modules.free_module import span
from sage.misc.misc_c import prod
cl... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/modular/abvar/lseries.py | 0.882908 | 0.585279 | lseries.py | pypi |
from sage.misc.lazy_import import lazy_import
from sage.rings.integer_ring import ZZ
from sage.rings.rational_field import QQ
from sage.modular.modform.element import Newform
from sage.modular.arithgroup.all import is_Gamma0, is_Gamma1, is_GammaH
from .abvar import ModularAbelianVariety_modsym_abstract
from . import... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/modular/abvar/abvar_newform.py | 0.737914 | 0.365513 | abvar_newform.py | pypi |
from copy import copy
from sage.categories.homset import HomsetWithBase
from sage.structure.all import parent
from sage.misc.lazy_attribute import lazy_attribute
from . import morphism
import sage.rings.integer_ring
import sage.rings.all
from sage.rings.ring import Ring
from sage.matrix.matrix_space import Matri... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/modular/abvar/homspace.py | 0.759315 | 0.46223 | homspace.py | pypi |
from sage.structure.element import ModuleElement
from sage.structure.richcmp import richcmp, rich_to_bool
class TorsionPoint(ModuleElement):
r"""
An element of a finite subgroup of a modular abelian variety.
INPUT:
- ``parent`` -- a finite subgroup of a modular abelian variety
- ``element`` --... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/modular/abvar/torsion_point.py | 0.943138 | 0.693753 | torsion_point.py | pypi |
import weakref
from sage.rings.integer import Integer
from sage.modular.arithgroup.all import is_CongruenceSubgroup, Gamma0
from sage.modular.modsym.space import is_ModularSymbolsSpace
from .abvar_newform import ModularAbelianVariety_newform
import sage.modular.modform.element
from . import abvar
_cache = {}
def _... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/modular/abvar/constructor.py | 0.712132 | 0.531392 | constructor.py | pypi |
r"""
Universal cyclotomic field
The universal cyclotomic field is the smallest subfield of the complex field
containing all roots of unity. It is also the maximal Galois Abelian extension
of the rational numbers.
The implementation simply wraps GAP Cyclotomic. As mentioned in their
documentation: arithmetical operati... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/universal_cyclotomic_field.py | 0.895668 | 0.728435 | universal_cyclotomic_field.py | pypi |
r"""
Signed and Unsigned Infinities
The unsigned infinity "ring" is the set of two elements
1. infinity
2. A number less than infinity
The rules for arithmetic are that the unsigned infinity ring does
not canonically coerce to any other ring, and all other rings
canonically coerce to the unsigned infinity ring, sen... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/infinity.py | 0.866557 | 0.689175 | infinity.py | pypi |
from sage.misc.decorators import decorator_keywords, sage_wraps
@decorator_keywords
def handle_AA_and_QQbar(func):
r"""
Decorator to call a function that only accepts arguments in number fields.
The argument list is scanned for ideals and/or polynomials over algebraic
fields (``QQbar`` or ``AA``). If... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/qqbar_decorators.py | 0.939255 | 0.696532 | qqbar_decorators.py | pypi |
from sage.structure.parent import Parent
import sage.rings.integer_ring
from . import ideal
from sage.categories.monoids import Monoids
def IdealMonoid(R):
r"""
Return the monoid of ideals in the ring ``R``.
EXAMPLES::
sage: R = QQ['x']
sage: sage.rings.ideal_monoid.IdealMonoid(R)
... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/ideal_monoid.py | 0.872605 | 0.676206 | ideal_monoid.py | pypi |
r"""
Algebraic closures of finite fields
Let `\Bold{F}` be a finite field, and let `\overline{\Bold{F}}` be an
algebraic closure of `\Bold{F}`; this is unique up to (non-canonical)
isomorphism. For every `n\ge 1`, there is a unique subfield
`\Bold{F}_n` of `\overline{\Bold{F}}` such that
`\Bold{F}\subset\Bold{F}_n` a... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/algebraic_closure_finite_field.py | 0.900312 | 0.815637 | algebraic_closure_finite_field.py | pypi |
import sage.libs.pari.all as pari
import sage.rings.ring as ring
from sage.structure.element import RingElement
from sage.structure.richcmp import richcmp
from sage.misc.fast_methods import Singleton
class Pari(RingElement):
"""
Element of Pari pseudo-ring.
"""
def __init__(self, x, parent=None):
... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/pari_ring.py | 0.821617 | 0.460774 | pari_ring.py | pypi |
import sage.arith.all as arith
from . import laurent_series_ring_element
from sage.rings.puiseux_series_ring_element import PuiseuxSeries
import sage.rings.padics.factory as padics_factory
import sage.rings.padics.padic_generic_element as padic_generic_element
from . import power_series_ring_element
from . import integ... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/big_oh.py | 0.736401 | 0.640847 | big_oh.py | pypi |
from sage.categories.rings import Rings
from sage.rings.infinity import infinity
from sage.categories.algebras import Algebras
from sage.categories.integral_domains import IntegralDomains
from sage.categories.fields import Fields
from sage.categories.complete_discrete_valuation import CompleteDiscreteValuationFields
... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/laurent_series_ring.py | 0.921931 | 0.515559 | laurent_series_ring.py | pypi |
from sage.categories.homset import HomsetWithBase
from sage.categories.rings import Rings
_Rings = Rings()
from . import morphism
from . import quotient_ring
def is_RingHomset(H):
"""
Return ``True`` if ``H`` is a space of homomorphisms between two rings.
EXAMPLES::
sage: from sage.rings.homset... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/homset.py | 0.855504 | 0.551695 | homset.py | pypi |
r"""
Generic data structures and algorithms for rings
AUTHORS:
- Lorenz Panny (2022): :class:`ProductTree`, :func:`prod_with_derivative`
"""
from sage.misc.misc_c import prod
class ProductTree:
r"""
A simple binary product tree, i.e., a tree of ring elements in
which every node equals the product of it... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/generic.py | 0.913722 | 0.756425 | generic.py | pypi |
from sage.categories.morphism import Morphism
from sage.categories.homset import Hom
from .generic_nodes import pAdicFixedModRingGeneric, pAdicCappedAbsoluteRingGeneric, pAdicCappedRelativeRingGeneric, pAdicCappedRelativeFieldGeneric, pAdicFloatingPointRingGeneric, pAdicFloatingPointFieldGeneric
from .eisenstein_exten... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/padics/relative_extension_leaves.py | 0.799951 | 0.338159 | relative_extension_leaves.py | pypi |
r"""
Introduction to the `p`-adics
==========================================
This tutorial outlines what you need to know in order to use
`p`-adics in Sage effectively.
Our goal is to create a rich structure of different options that
will reflect the mathematical structures of the `p`-adics.
This is very much a work... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/padics/tutorial.py | 0.936256 | 0.976957 | tutorial.py | pypi |
import os
import sage.misc.misc
def coefficients_to_power_sums(n, m, a):
r"""
Takes the list a, representing a list of initial coefficients of
a (monic) polynomial of degree n, and returns the power sums
of the roots of f up to (m-1)th powers.
INPUT:
- n -- integer, the degree
- a -- li... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/number_field/totallyreal_phc.py | 0.538983 | 0.69938 | totallyreal_phc.py | pypi |
from sage.misc.cachefunc import cached_method
from sage.misc.superseded import deprecation
from sage.rings.homset import RingHomset_generic
from sage.rings.number_field.morphism import (NumberFieldHomomorphism_im_gens,
RelativeNumberFieldHomomorphism_from_abs,
... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/number_field/homset.py | 0.908305 | 0.535281 | homset.py | pypi |
from sage.misc.latex import latex
from sage.structure.unique_representation import UniqueRepresentation
from sage.structure.parent import Parent
from sage.structure.element import ModuleElement
from sage.structure.richcmp import richcmp
from sage.sets.family import Family
from sage.categories.modules import Modules
... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/function_field/differential.py | 0.916283 | 0.603757 | differential.py | pypi |
r"""
Special extensions of function fields
This module currently implements only constant field extension.
Constant field extensions
-------------------------
EXAMPLES:
Constant field extension of the rational function field over rational numbers::
sage: K.<x> = FunctionField(QQ)
sage: N.<a> = QuadraticFie... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/function_field/extensions.py | 0.907999 | 0.748513 | extensions.py | pypi |
from sage.rings.finite_rings.finite_field_base import FiniteField as FiniteField_generic
from sage.categories.finite_fields import FiniteFields
_FiniteFields = FiniteFields()
import sage.rings.finite_rings.integer_mod_ring as integer_mod_ring
from sage.rings.integer import Integer
import sage.rings.finite_rings.integ... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/finite_rings/finite_field_prime_modn.py | 0.918923 | 0.438004 | finite_field_prime_modn.py | pypi |
from sage.rings.finite_rings.finite_field_base import FiniteField
from sage.rings.integer import Integer
from sage.rings.finite_rings.element_givaro import Cache_givaro
from sage.libs.pari.all import pari
from sage.misc.superseded import deprecated_function_alias
class FiniteField_givaro(FiniteField):
"""
Fi... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/finite_rings/finite_field_givaro.py | 0.921019 | 0.513425 | finite_field_givaro.py | pypi |
from sage.rings.finite_rings.finite_field_base import FiniteField
from sage.libs.pari.all import pari
from sage.rings.integer import Integer
from sage.misc.superseded import deprecated_function_alias
def late_import():
"""
Imports various modules after startup.
EXAMPLES::
sage: sage.rings.finite... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/finite_rings/finite_field_ntl_gf2e.py | 0.883958 | 0.449211 | finite_field_ntl_gf2e.py | pypi |
from .element_pari_ffelt import FiniteFieldElement_pari_ffelt
from .finite_field_base import FiniteField
from .finite_field_constructor import GF
class FiniteField_pari_ffelt(FiniteField):
"""
Finite fields whose cardinality is a prime power (not a prime),
implemented using PARI's ``FFELT`` type.
IN... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/finite_rings/finite_field_pari_ffelt.py | 0.905375 | 0.650273 | finite_field_pari_ffelt.py | pypi |
r"""
Galois groups of Finite Fields
"""
from sage.groups.abelian_gps.abelian_group_element import AbelianGroupElement
from sage.groups.galois_group import GaloisGroup_cyc
from sage.rings.integer_ring import ZZ
from sage.rings.finite_rings.hom_finite_field import FiniteFieldHomomorphism_generic, FrobeniusEndomorphism_f... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/finite_rings/galois_group.py | 0.894332 | 0.595287 | galois_group.py | pypi |
from sage.categories.morphism import Morphism
class FiniteFieldVectorSpaceIsomorphism(Morphism):
"""
Base class of the vector space isomorphism between a finite field
and a vector space over a subfield of the finite field.
"""
def _repr_(self):
"""
Return the string representation ... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/finite_rings/maps_finite_field.py | 0.884533 | 0.676854 | maps_finite_field.py | pypi |
r"""
Educational versions of Groebner basis algorithms: triangular factorization
In this file is the implementation of two algorithms in [Laz1992]_.
The main algorithm is ``Triangular``; a secondary algorithm, necessary for the
first, is ``ElimPolMin``. As per Lazard's formulation, the implementation works
with any t... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/polynomial/toy_variety.py | 0.949424 | 0.887156 | toy_variety.py | pypi |
from copy import copy
from sage.rings.complex_mpfr import ComplexField
from sage.rings.complex_interval_field import ComplexIntervalField
from sage.rings.qqbar import AA, QQbar
from sage.arith.misc import sort_complex_numbers_for_display
from sage.rings.polynomial.refine_root import refine_root
def interval_roots(... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/polynomial/complex_roots.py | 0.761272 | 0.682858 | complex_roots.py | pypi |
r"""
Educational version of the `d`-Groebner basis algorithm over PIDs
No attempt was made to optimize this algorithm as the emphasis of this
implementation is a clean and easy presentation.
.. NOTE::
The notion of 'term' and 'monomial' in [BW1993]_ is swapped from the
notion of those words in Sage (or the o... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/polynomial/toy_d_basis.py | 0.925496 | 0.825555 | toy_d_basis.py | pypi |
r"""
Polynomial Sequences
We call a finite list of polynomials a ``Polynomial Sequence``.
Polynomial sequences in Sage can optionally be viewed as consisting of
various parts or sub-sequences. These kind of polynomial sequences
which naturally split into parts arise naturally for example in
algebraic cryptanalysis of... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/polynomial/multi_polynomial_sequence.py | 0.844553 | 0.734143 | multi_polynomial_sequence.py | pypi |
from sage.rings.polynomial.polynomial_element import Polynomial_generic_dense, Polynomial
from sage.rings.polynomial.padics.polynomial_padic import Polynomial_padic
from sage.rings.infinity import infinity
from sage.libs.pari.all import pari_gen
import sage.rings.padics.misc
class Polynomial_padic_flat(Polynomial_gen... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/polynomial/padics/polynomial_padic_flat.py | 0.787319 | 0.483526 | polynomial_padic_flat.py | pypi |
from .pbori import (top_index, if_then_else,
mod_mon_set, BooleSet, BooleConstant)
from .PyPolyBoRi import (Polynomial, Monomial, Variable)
def all_monomials_of_degree_d_old(d, variables):
"""
Return monomials of degree d in the given variables.
Obsolete version ?
"""
if d == ... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/polynomial/pbori/specialsets.py | 0.707809 | 0.61927 | specialsets.py | pypi |
r"""
PolyBoRi's interface to libpolybori/BRiAL
This file makes interfaces to PolyBoRi's runtime libraries available in Python via sage.
AUTHOR:
- The PolyBoRi Team, 2007-2012
EXAMPLES::
sage: from sage.rings.polynomial.pbori.pbori import *
sage: from sage.rings.polynomial.pbori.blocks import d... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/polynomial/pbori/PyPolyBoRi.py | 0.553626 | 0.702288 | PyPolyBoRi.py | pypi |
from random import Random
from sage.rings.polynomial.pbori.pbori import if_then_else as ite
from .PyPolyBoRi import Polynomial
from .statistics import used_vars_set
class CNFEncoder():
def __init__(self, r, random_seed=16):
self.random_generator = Random(random_seed)
self.one_set = r.one().set()
... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/polynomial/pbori/cnf.py | 0.514644 | 0.442998 | cnf.py | pypi |
r"""
parallel.py
PolyBoRi
Created by Michael Brickenstein on 2008-10-31.
Copyright 2008 The PolyBoRi Team
"""
from zlib import compress, decompress
import copyreg
from .pbori import if_then_else, BooleSet, CCuddNavigator
from .PyPolyBoRi import (Polynomial, Ring, WeakRingRef, Monomial, Variable)
from .gbcore import g... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/polynomial/pbori/parallel.py | 0.673406 | 0.68616 | parallel.py | pypi |
from .pbori import (top_index, if_then_else,
substitute_variables, BooleSet,
ll_red_nf_redsb, ll_red_nf_noredsb,
ll_red_nf_noredsb_single_recursive_call)
from .PyPolyBoRi import (Polynomial, Monomial, Ring, BoolePolynomialVector)
from .statistics import used_v... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/polynomial/pbori/ll.py | 0.459319 | 0.496521 | ll.py | pypi |
from random import Random
from pprint import pformat
from .PyPolyBoRi import (Monomial, Polynomial, Variable)
from .pbori import random_set, set_random_seed, ll_red_nf_redsb
from .ll import ll_encode
from .blocks import declare_ring
def gen_random_poly(ring, l, deg, vars_set, seed=123):
"""
Generate a random... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/polynomial/pbori/randompoly.py | 0.645008 | 0.550547 | randompoly.py | pypi |
from .PyPolyBoRi import Polynomial, BoolePolynomialVector
from .pbori import FGLMStrategy, BooleSet
def _fglm(I, from_ring, to_ring):
r"""
Unchecked variant of fglm
"""
vec = BoolePolynomialVector(I)
return FGLMStrategy(from_ring, to_ring, vec).main()
def fglm(I, from_ring, to_ring):
r"""
... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/polynomial/pbori/fglm.py | 0.837686 | 0.678194 | fglm.py | pypi |
from sage.misc.lazy_import import lazy_import
from .PyPolyBoRi import Ring, Polynomial, Monomial, Variable
# Get all-inclusive groebner routine
from .gbcore import groebner_basis
from .nf import normal_form
# Import some high-level modelling functionality
from .blocks import declare_ring
from .blocks import HigherOrd... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/polynomial/pbori/__init__.py | 0.474388 | 0.17971 | __init__.py | pypi |
from time import process_time as clock
from random import Random
from .PyPolyBoRi import (Polynomial, Variable, Monomial,
BoolePolynomialVector)
from .randompoly import gen_random_poly
from .pbori import (BooleSet, add_up_polynomials, interpolate_smallest_lex,
interpolate)
... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/rings/polynomial/pbori/interpolate.py | 0.624866 | 0.576363 | interpolate.py | pypi |
from sage.misc.superseded import deprecation
from sage.modules.free_module_element import vector
from sage.rings.real_double import RDF
def find_root(f, a, b, xtol=10e-13, rtol=2.0**-50, maxiter=100, full_output=False):
r"""
Numerically find a root of ``f`` on the closed interval `[a,b]`
(or `[b,a]`) if p... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/numerical/optimize.py | 0.930954 | 0.716281 | optimize.py | pypi |
r"""
Base classes for reflexive modules
"""
from sage.misc.abstract_method import abstract_method
from sage.structure.parent import Parent
class ReflexiveModule_abstract(Parent):
r"""
Abstract base class for reflexive modules.
An `R`-module `M` is *reflexive* if the natural map from `M` to its double
... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/tensor/modules/reflexive_module.py | 0.942009 | 0.820613 | reflexive_module.py | pypi |
from sage.algebras.iwahori_hecke_algebra import IwahoriHeckeAlgebra
from sage.combinat.sf.sf import SymmetricFunctions
from sage.misc.misc_c import prod
from sage.rings.rational_field import QQ
from sage.combinat.partition import Partitions
class NilCoxeterAlgebra(IwahoriHeckeAlgebra.T):
r"""
Construct the Nil... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/algebras/nil_coxeter_algebra.py | 0.881028 | 0.495484 | nil_coxeter_algebra.py | pypi |
from sage.misc.cachefunc import cached_method
from sage.categories.magmatic_algebras import MagmaticAlgebras
from sage.categories.magmas import Magmas
from sage.categories.pushout import (ConstructionFunctor,
CompositeConstructionFunctor,
Identit... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/algebras/free_zinbiel_algebra.py | 0.85738 | 0.521349 | free_zinbiel_algebra.py | pypi |
from sage.misc.cachefunc import cached_method
from sage.rings.polynomial.laurent_polynomial_ring import LaurentPolynomialRing
from sage.rings.rational_field import QQ
from sage.categories.algebras import Algebras
from sage.categories.rings import Rings
from sage.combinat.free_module import CombinatorialFreeModule
from... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/algebras/yokonuma_hecke_algebra.py | 0.917006 | 0.697301 | yokonuma_hecke_algebra.py | pypi |
from sage.misc.repr import repr_lincomb
from sage.structure.element import RingElement, AlgebraElement
from sage.structure.parent_gens import localvars
from sage.structure.richcmp import richcmp
from sage.rings.integer import Integer
from sage.modules.free_module_element import FreeModuleElement
from sage.monoids.free... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/algebras/free_algebra_quotient_element.py | 0.780662 | 0.385519 | free_algebra_quotient_element.py | pypi |
from sage.misc.cachefunc import cached_method
from sage.misc.lazy_attribute import lazy_attribute
from sage.categories.algebras import Algebras
from sage.combinat.free_module import CombinatorialFreeModule
from sage.combinat.root_system.cartan_type import CartanType
from sage.combinat.root_system.cartan_matrix import ... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/algebras/rational_cherednik_algebra.py | 0.840488 | 0.610366 | rational_cherednik_algebra.py | pypi |
r"""
Catalog of Algebras
The ``algebras`` object may be used to access examples of various algebras
currently implemented in Sage. Using tab-completion on this object is an
easy way to discover and quickly create the algebras that are available
(as listed here).
Let ``<tab>`` indicate pressing the :kbd:`Tab` key. So... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/algebras/catalog.py | 0.865821 | 0.662892 | catalog.py | pypi |
from sage.modules.free_module import FreeModule
from sage.rings.ring import Algebra
from sage.algebras.free_algebra import is_FreeAlgebra
from sage.algebras.free_algebra_quotient_element import FreeAlgebraQuotientElement
from sage.structure.unique_representation import UniqueRepresentation
class FreeAlgebraQuotient(... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/algebras/free_algebra_quotient.py | 0.73848 | 0.333883 | free_algebra_quotient.py | pypi |
from sage.categories.all import AlgebrasWithBasis
from sage.combinat.root_system.cartan_type import CartanType
from sage.combinat.root_system.weyl_group import WeylGroup
from sage.rings.ring import Ring
from sage.rings.integer_ring import ZZ
from sage.combinat.free_module import CombinatorialFreeModule
from sage.misc.c... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/algebras/affine_nil_temperley_lieb.py | 0.822046 | 0.641394 | affine_nil_temperley_lieb.py | pypi |
from sage.misc.cachefunc import cached_method
from sage.categories.algebras import Algebras
from sage.categories.cartesian_product import cartesian_product
from sage.categories.rings import Rings
from sage.combinat.free_module import CombinatorialFreeModule
from sage.modules.with_basis.morphism import ModuleMorphismBy... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/algebras/askey_wilson.py | 0.895902 | 0.689378 | askey_wilson.py | pypi |
from sage.misc.cachefunc import cached_method
from sage.misc.lazy_attribute import lazy_attribute
from sage.categories.algebras import Algebras
from sage.combinat.free_module import CombinatorialFreeModule
from sage.monoids.indexed_free_monoid import IndexedFreeAbelianMonoid
from sage.sets.positive_integers import Pos... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/algebras/quantum_groups/ace_quantum_onsager.py | 0.686895 | 0.596698 | ace_quantum_onsager.py | pypi |
from .finite_dimensional_algebra_element import FiniteDimensionalAlgebraElement
from .finite_dimensional_algebra_ideal import FiniteDimensionalAlgebraIdeal
from sage.rings.integer_ring import ZZ
from sage.categories.magmatic_algebras import MagmaticAlgebras
from sage.matrix.constructor import Matrix, matrix
from sag... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/algebras/finite_dimensional_algebras/finite_dimensional_algebra.py | 0.924743 | 0.699928 | finite_dimensional_algebra.py | pypi |
from sage.misc.cachefunc import cached_method
from sage.rings.morphism import RingHomomorphism_im_gens
from sage.rings.homset import RingHomset_generic
from sage.structure.element import is_Matrix
class FiniteDimensionalAlgebraMorphism(RingHomomorphism_im_gens):
"""
Create a morphism between two :class:`fini... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/algebras/finite_dimensional_algebras/finite_dimensional_algebra_morphism.py | 0.904255 | 0.698426 | finite_dimensional_algebra_morphism.py | pypi |
from .finite_dimensional_algebra_element import FiniteDimensionalAlgebraElement
from sage.matrix.constructor import Matrix
from sage.structure.element import is_Matrix
from sage.rings.ideal import Ideal_generic
from sage.structure.element import parent
from sage.misc.cachefunc import cached_method
from functools imp... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/algebras/finite_dimensional_algebras/finite_dimensional_algebra_ideal.py | 0.900327 | 0.68975 | finite_dimensional_algebra_ideal.py | pypi |
from sage.arith.all import factorial
from sage.misc.misc_c import prod
from sage.misc.repr import repr_lincomb
from sage.misc.latex import latex
from sage.modules.with_basis.indexed_element import IndexedFreeModuleElement
class LCAWithGeneratorsElement(IndexedFreeModuleElement):
"""
The element class of a Lie... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/algebras/lie_conformal_algebras/lie_conformal_algebra_element.py | 0.742982 | 0.517144 | lie_conformal_algebra_element.py | pypi |
from sage.misc.cachefunc import cached_method
from sage.structure.element import get_coercion_model
from operator import mul
from sage.categories.algebras import Algebras
from sage.monoids.indexed_free_monoid import IndexedFreeAbelianMonoid
from sage.combinat.free_module import CombinatorialFreeModule
from sage.sets.f... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/algebras/lie_algebras/poincare_birkhoff_witt.py | 0.897819 | 0.575916 | poincare_birkhoff_witt.py | pypi |
r"""
Scheme implementation overview
Various parts of schemes were implemented by different authors. This document
aims to give an overview of the different classes of schemes working together
coherently.
Generic
-------
- **Scheme:**
A scheme whose datatype might not be defined in terms of algebraic equations:
e... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/overview.py | 0.952386 | 0.86293 | overview.py | pypi |
from sage.schemes.generic.morphism import SchemeMorphism_polynomial
class WeierstrassTransformation(SchemeMorphism_polynomial):
def __init__(self, domain, codomain, defining_polynomials, post_multiplication):
r"""
A morphism of a genus-one curve to/from the Weierstrass form.
INPUT:
... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/elliptic_curves/weierstrass_transform.py | 0.952816 | 0.651204 | weierstrass_transform.py | pypi |
from .ell_field import EllipticCurve_field
from . import ell_point
from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
# Elliptic curves are very different than genus > 1 hyperelliptic curves,
# there is an "is a" relationship here, and common implementation with regard
# Coleman integration.... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/elliptic_curves/ell_padic_field.py | 0.782164 | 0.513181 | ell_padic_field.py | pypi |
r"""
Scalar-multiplication morphisms of elliptic curves
This class provides an :class:`EllipticCurveHom` instantiation for
multiplication-by-`m` maps on elliptic curves.
EXAMPLES:
We can construct and evaluate scalar multiplications::
sage: from sage.schemes.elliptic_curves.hom_scalar import EllipticCurveHom_sc... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/elliptic_curves/hom_scalar.py | 0.87105 | 0.842151 | hom_scalar.py | pypi |
r"""
Frobenius isogenies of elliptic curves
Frobenius isogenies only exist in positive characteristic `p`. They
are given by `\pi_n:(x,y)\mapsto (x^{p^n},y^{p^n})`.
This class implements `\pi_n` for `n \geq 0`. Together with existing
tools for composing isogenies (see :class:`EllipticCurveHom_composite`),
we can ther... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/elliptic_curves/hom_frobenius.py | 0.884046 | 0.712745 | hom_frobenius.py | pypi |
from sage.structure.parent_gens import localvars
from sage.interfaces.gp import Gp
from sage.misc.sage_eval import sage_eval
from sage.misc.randstate import current_randstate
from sage.rings.integer_ring import ZZ
from sage.rings.rational_field import QQ
gp = None
def init():
"""
Function to initialize the ... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/elliptic_curves/gp_simon.py | 0.610686 | 0.397675 | gp_simon.py | pypi |
from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
from sage.rings.rational_field import QQ
from .constructor import EllipticCurve
def mod5family(a, b):
"""
Formulas for computing the family of elliptic curves with
congruent mod-5 representation.
EXAMPLES::
sage: f... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/elliptic_curves/mod5family.py | 0.481698 | 0.703359 | mod5family.py | pypi |
r"""
Tables of elliptic curves of given rank
The default database of curves contains the following data:
+------+------------------+--------------------+
| Rank | Number of curves | Maximal conductor |
+======+==================+====================+
| 0 | 30427 | 9999 |
+------+---------... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/elliptic_curves/ec_database.py | 0.886377 | 0.735784 | ec_database.py | pypi |
r"""
Berkovich Space over `\CC_p`
The Berkovich affine line is the set of seminorms on `\CC_p[x]`,
with the weakest topology that makes the map `| \cdot | \to |f|` continuous
for all `f \in \CC_p[x]`. The Berkovich projective line is the
one-point compactification of the Berkovich affine line.
The two main classes ar... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/berkovich/berkovich_space.py | 0.934574 | 0.69382 | berkovich_space.py | pypi |
r"""
Cyclic covers over a finite field
The most interesting feature is computation of Frobenius matrix on
Monsky-Washnitzer cohomology and the Frobenius polynomial.
REFERENCES:
- [ABCMT2019]_
EXAMPLES::
sage: p = 13
sage: x = PolynomialRing(GF(p),"x").gen()
sage: C = CyclicCover(4, x^4 + 1)
sage: ... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/cyclic_covers/cycliccover_finite_field.py | 0.762689 | 0.768625 | cycliccover_finite_field.py | pypi |
from sage.rings.polynomial.polynomial_element import is_Polynomial
from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
from sage.schemes.affine.affine_space import AffineSpace
from .cycliccover_generic import CyclicCover_generic
from .cycliccover_finite_field import CyclicCover_finite_field
d... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/cyclic_covers/constructor.py | 0.923549 | 0.767886 | constructor.py | pypi |
from sage.rings.polynomial.all import PolynomialRing
from sage.structure.category_object import normalize_names
from sage.arith.misc import GCD
from sage.schemes.curves.affine_curve import AffinePlaneCurve
class CyclicCover_generic(AffinePlaneCurve):
def __init__(self, AA, r, f, names=None):
"""
... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/cyclic_covers/cycliccover_generic.py | 0.851413 | 0.616012 | cycliccover_generic.py | pypi |
r"""
Points of bounded height in projective spaces
This module defines functions to compute points of bounded height of a given
number field with height less than a specified bound in projective spaces.
Sage functions to list all elements of a given number field with height less
than a specified bound.
AUTHORS:
- J... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/projective/proj_bdd_height.py | 0.930836 | 0.781372 | proj_bdd_height.py | pypi |
from sage.categories.fields import Fields
_Fields = Fields()
from sage.schemes.generic.scheme import Scheme, is_Scheme
from sage.structure.richcmp import richcmp_method, richcmp
def is_Jacobian(J):
"""
Return True if `J` is of type Jacobian_generic.
EXAMPLES::
sage: from sage.schemes.jacobians.a... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/jacobians/abstract_jacobian.py | 0.925407 | 0.632105 | abstract_jacobian.py | pypi |
from sage.misc.latex import latex
from sage.categories.finite_fields import FiniteFields
from sage.categories.fields import Fields
from sage.schemes.generic.algebraic_scheme import AlgebraicScheme_subscheme
from sage.schemes.generic.divisor_group import DivisorGroup
from sage.schemes.generic.divisor import Divisor_c... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/curves/curve.py | 0.946631 | 0.603961 | curve.py | pypi |
from sage.structure.richcmp import richcmp
from sage.schemes.generic.point import SchemeTopologicalPoint_prime_ideal
class CurveClosedPoint(SchemeTopologicalPoint_prime_ideal):
"""
Base class of closed points of curves.
"""
pass
class IntegralCurveClosedPoint(CurveClosedPoint):
"""
Closed p... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/curves/closed_point.py | 0.939775 | 0.736851 | closed_point.py | pypi |
from sage.categories.fields import Fields
from sage.rings.polynomial.multi_polynomial_element import is_MPolynomial
from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing
from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
from sage.rings.rational_field import QQ
from sag... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/curves/constructor.py | 0.921838 | 0.532425 | constructor.py | pypi |
from sage.schemes.affine.affine_point import (SchemeMorphism_point_affine_field,
SchemeMorphism_point_affine_finite_field)
from sage.schemes.projective.projective_point import (SchemeMorphism_point_projective_field,
Sche... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/curves/point.py | 0.922159 | 0.581927 | point.py | pypi |
from sage.rings.polynomial.all import PolynomialRing
from sage.rings.big_oh import O
from sage.rings.power_series_ring import PowerSeriesRing
from sage.rings.laurent_series_ring import LaurentSeriesRing
from sage.rings.real_mpfr import RR
from sage.functions.all import log
from sage.structure.category_object import no... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/hyperelliptic_curves/hyperelliptic_generic.py | 0.813387 | 0.623176 | hyperelliptic_generic.py | pypi |
from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
from sage.rings.integer_ring import ZZ
from sage.rings.integer import is_Integer, Integer
from sage.rings.polynomial.polynomial_element import is_Polynomial
from sage.schemes.generic.homset import SchemeHomset_points
from sage.schemes.generi... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/hyperelliptic_curves/jacobian_homset.py | 0.902074 | 0.606032 | jacobian_homset.py | pypi |
r"""
Compute invariants of quintics and sextics via 'Ueberschiebung'
.. TODO::
* Implement invariants in small positive characteristic.
* Cardona-Quer and additional invariants for classifying automorphism groups.
AUTHOR:
- Nick Alexander
"""
from sage.rings.integer_ring import ZZ
from sage.rings.polynomi... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/hyperelliptic_curves/invariants.py | 0.70028 | 0.909103 | invariants.py | pypi |
from sage.schemes.projective.projective_space import ProjectiveSpace
from .hyperelliptic_generic import HyperellipticCurve_generic
from .hyperelliptic_finite_field import HyperellipticCurve_finite_field
from .hyperelliptic_rational_field import HyperellipticCurve_rational_field
from .hyperelliptic_padic_field import ... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/hyperelliptic_curves/constructor.py | 0.935013 | 0.618838 | constructor.py | pypi |
r"""
Jacobian 'morphism' as a class in the Picard group
This module implements the group operation in the Picard group of a
hyperelliptic curve, represented as divisors in Mumford
representation, using Cantor's algorithm.
A divisor on the hyperelliptic curve `y^2 + y h(x) = f(x)`
is stored in Mumford representation, ... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/hyperelliptic_curves/jacobian_morphism.py | 0.897485 | 0.916559 | jacobian_morphism.py | pypi |
from sage.misc.latex import latex
from sage.misc.repr import repr_lincomb
from sage.misc.search import search
from sage.rings.integer_ring import ZZ
from sage.structure.formal_sum import FormalSum
from .morphism import is_SchemeMorphism
from sage.schemes.affine.affine_space import is_AffineSpace
from sage.schemes.pro... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/generic/divisor.py | 0.78968 | 0.39129 | divisor.py | pypi |
from sage.structure.parent import Parent
from sage.misc.cachefunc import cached_method
from sage.rings.integer_ring import ZZ
from sage.categories.commutative_rings import CommutativeRings
from sage.rings.ideal import is_Ideal
from sage.structure.unique_representation import UniqueRepresentation
from sage.schemes.gene... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/generic/scheme.py | 0.915642 | 0.51879 | scheme.py | pypi |
from sage.categories.functor import Functor
from sage.rings.integer_ring import ZZ
from sage.schemes.generic.scheme import AffineScheme
from sage.structure.unique_representation import UniqueRepresentation
def Spec(R, S=None):
r"""
Apply the Spec functor to `R`.
INPUT:
- ``R`` -- either a commutati... | /sagemath-standard-10.0b0.tar.gz/sagemath-standard-10.0b0/sage/schemes/generic/spec.py | 0.929911 | 0.475971 | spec.py | pypi |
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