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def text3d(txt, (x,y,z), **kwds): r""" Display 3d text. INPUT: - ``txt`` - some text - ``(x,y,z)`` - position - ``**kwds`` - standard 3d graphics options .. note:: There is no way to change the font size or opacity yet. EXAMPLES: We write the word Sage in red at position (1,2,3):: sage: text3d("Sage", (1,2...
def text3d(txt, (x,y,z), **kwds): r""" Display 3d text. INPUT: - ``txt`` - some text - ``(x,y,z)`` - position - ``**kwds`` - standard 3d graphics options .. note:: There is no way to change the font size or opacity yet. EXAMPLES: We write the word Sage in red at position (1,2,3):: sage: text3d("Sage", (1,2...
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def text3d(txt, (x,y,z), **kwds): r""" Display 3d text. INPUT: - ``txt`` - some text - ``(x,y,z)`` - position - ``**kwds`` - standard 3d graphics options .. note:: There is no way to change the font size or opacity yet. EXAMPLES: We write the word Sage in red at position (1,2,3):: sage: text3d("Sage", (1,2...
deftext3d(txt,(x,y,z),**kwds):r"""Display3dtext.INPUT:-``txt``-sometext-``(x,y,z)``-position-``**kwds``-standard3dgraphicsoptions..note::Thereisnowaytochangethefontsizeoropacityyet.EXAMPLES:WewritethewordSageinredatposition(1,2,3)::sage:text3d("Sage",(1,2,3),color=(0.5,0,0))Wedrawamulticolorspiralofnumbers::sage:sum([t...
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def __init__(self, center, size=1, **kwds): """ Create the graphics primitive :class:`Point` in 3D. See the docstring of this class for full documentation.
def __init__(self, center, size=1, **kwds): """ Create the graphics primitive :class:`Point` in 3-D. See the docstring of this class for full documentation.
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def bounding_box(self): """ Returns the lower and upper corners of a 3D bounding box for self. This is used for rendering and self should fit entirely within this box. In this case, we simply return the center of the point.
def bounding_box(self): """ Returns the lower and upper corners of a 3-D bounding box for ``self``. This is used for rendering and ``self`` should fit entirely within this box. In this case, we simply return the center of the point.
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def tachyon_repr(self, render_params): """ Returns representation of the point suitable for plotting using Tachyon ray tracer.
def tachyon_repr(self, render_params): """ Returns representation of the point suitable for plotting using Tachyon ray tracer.
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def __init__(self, points, thickness=5, corner_cutoff=.5, arrow_head=False, **kwds): """ Create the graphics primitive :class:`Line` in 3D. See the docstring of this class for full documentation.
def __init__(self, points, thickness=5, corner_cutoff=.5, arrow_head=False, **kwds): """ Create the graphics primitive :class:`Line` in 3-D. See the docstring of this class for full documentation.
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def bounding_box(self): """ Returns the lower and upper corners of a 3D bounding box for self. This is used for rendering and self should fit entirely within this box. In this case, we return the highest and lowest values of each coordinate among all points.
def bounding_box(self): """ Returns the lower and upper corners of a 3-D bounding box for ``self``. This is used for rendering and ``self`` should fit entirely within this box. In this case, we return the highest and lowest values of each coordinate among all points.
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def tachyon_repr(self, render_params): """ Returns representation of the line suitable for plotting using Tachyon ray tracer.
def tachyon_repr(self, render_params): """ Returns representation of the line suitable for plotting using Tachyon ray tracer.
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def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth): r""" ``region_plot`` takes a boolean function of two variables, `f(x,y)` and plots the region where f is True over the specified ``xrange`` and ``yrange`` as demonstrated below. ``region_plot(f, (xmin, xmax), (ymin, ym...
def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth): r""" ``region_plot`` takes a boolean function of two variables, `f(x,y)` and plots the region where f is True over the specified ``xrange`` and ``yrange`` as demonstrated below. ``region_plot(f, (xmin, xmax), (ymin, ym...
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def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth): r""" ``region_plot`` takes a boolean function of two variables, `f(x,y)` and plots the region where f is True over the specified ``xrange`` and ``yrange`` as demonstrated below. ``region_plot(f, (xmin, xmax), (ymin, ym...
def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth): r""" ``region_plot`` takes a boolean function of two variables, `f(x,y)` and plots the region where f is True over the specified ``xrange`` and ``yrange`` as demonstrated below. ``region_plot(f, (xmin, xmax), (ymin, ym...
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def equify(f, variables = None): """ Returns the equation rewritten as a symbolic function to give negative values when True, positive when False. EXAMPLES:: sage: from sage.plot.contour_plot import equify sage: var('x, y') (x, y) sage: equify(x^2 < 2) x |--> x^2 - 2 sage: equify(x^2 > 2) x |--> -x^2 + 2 sage: equify...
def equify(f): """ Returns the equation rewritten as a symbolic function to give negative values when True, positive when False. EXAMPLES:: sage: from sage.plot.contour_plot import equify sage: var('x, y') (x, y) sage: equify(x^2 < 2) x |--> x^2 - 2 sage: equify(x^2 > 2) x |--> -x^2 + 2 sage: equify(x*y > 1) (x, y) |...
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def equify(f, variables = None): """ Returns the equation rewritten as a symbolic function to give negative values when True, positive when False. EXAMPLES:: sage: from sage.plot.contour_plot import equify sage: var('x, y') (x, y) sage: equify(x^2 < 2) x |--> x^2 - 2 sage: equify(x^2 > 2) x |--> -x^2 + 2 sage: equify...
def equify(f, variables = None): """ Returns the equation rewritten as a symbolic function to give negative values when True, positive when False. EXAMPLES:: sage: from sage.plot.contour_plot import equify sage: var('x, y') (x, y) sage: equify(x^2 < 2) x^2 - 2 sage: equify(x^2 > 2) x |--> -x^2 + 2 sage: equify(x*y > ...
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def equify(f, variables = None): """ Returns the equation rewritten as a symbolic function to give negative values when True, positive when False. EXAMPLES:: sage: from sage.plot.contour_plot import equify sage: var('x, y') (x, y) sage: equify(x^2 < 2) x |--> x^2 - 2 sage: equify(x^2 > 2) x |--> -x^2 + 2 sage: equify...
def equify(f, variables = None): """ Returns the equation rewritten as a symbolic function to give negative values when True, positive when False. EXAMPLES:: sage: from sage.plot.contour_plot import equify sage: var('x, y') (x, y) sage: equify(x^2 < 2) x |--> x^2 - 2 sage: equify(x^2 > 2) -x^2 + 2 sage: equify(x*y > ...
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def equify(f, variables = None): """ Returns the equation rewritten as a symbolic function to give negative values when True, positive when False. EXAMPLES:: sage: from sage.plot.contour_plot import equify sage: var('x, y') (x, y) sage: equify(x^2 < 2) x |--> x^2 - 2 sage: equify(x^2 > 2) x |--> -x^2 + 2 sage: equify...
def equify(f, variables = None): """ Returns the equation rewritten as a symbolic function to give negative values when True, positive when False. EXAMPLES:: sage: from sage.plot.contour_plot import equify sage: var('x, y') (x, y) sage: equify(x^2 < 2) x |--> x^2 - 2 sage: equify(x^2 > 2) x |--> -x^2 + 2 sage: equify...
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def equify(f, variables = None): """ Returns the equation rewritten as a symbolic function to give negative values when True, positive when False. EXAMPLES:: sage: from sage.plot.contour_plot import equify sage: var('x, y') (x, y) sage: equify(x^2 < 2) x |--> x^2 - 2 sage: equify(x^2 > 2) x |--> -x^2 + 2 sage: equify...
def equify(f, variables = None): """ Returns the equation rewritten as a symbolic function to give negative values when True, positive when False. EXAMPLES:: sage: from sage.plot.contour_plot import equify sage: var('x, y') (x, y) sage: equify(x^2 < 2) x |--> x^2 - 2 sage: equify(x^2 > 2) x |--> -x^2 + 2 sage: equify...
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def equify(f, variables = None): """ Returns the equation rewritten as a symbolic function to give negative values when True, positive when False. EXAMPLES:: sage: from sage.plot.contour_plot import equify sage: var('x, y') (x, y) sage: equify(x^2 < 2) x |--> x^2 - 2 sage: equify(x^2 > 2) x |--> -x^2 + 2 sage: equify...
def equify(f, variables = None): """ Returns the equation rewritten as a symbolic function to give negative values when True, positive when False. EXAMPLES:: sage: from sage.plot.contour_plot import equify sage: var('x, y') (x, y) sage: equify(x^2 < 2) x |--> x^2 - 2 sage: equify(x^2 > 2) x |--> -x^2 + 2 sage: equify...
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def equify(f, variables = None): """ Returns the equation rewritten as a symbolic function to give negative values when True, positive when False. EXAMPLES:: sage: from sage.plot.contour_plot import equify sage: var('x, y') (x, y) sage: equify(x^2 < 2) x |--> x^2 - 2 sage: equify(x^2 > 2) x |--> -x^2 + 2 sage: equify...
def equify(f, variables = None): """ Returns the equation rewritten as a symbolic function to give negative values when True, positive when False. EXAMPLES:: sage: from sage.plot.contour_plot import equify sage: var('x, y') (x, y) sage: equify(x^2 < 2) x |--> x^2 - 2 sage: equify(x^2 > 2) x |--> -x^2 + 2 sage: equify...
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def univariate_polynomial(self, R=None): """ Returns a univariate polynomial associated to this multivariate polynomial. INPUT: - ``R`` - (default: None) PolynomialRing If this polynomial is not in at most one variable, then a ValueError exception is raised. This is checked using the is_univariate() method. The n...
def univariate_polynomial(self, R=None): """ Returns a univariate polynomial associated to this multivariate polynomial. INPUT: - ``R`` - (default: None) PolynomialRing If this polynomial is not in at most one variable, then a ValueError exception is raised. This is checked using the is_univariate() method. The n...
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def quotient(self, sub, check=True): """ Return the quotient of ``self`` by the given sublattice ``sub``. INPUT:
def quotient(self, sub, check=True, positive_point=None, positive_dual_point=None): """ Return the quotient of ``self`` by the given sublattice ``sub``. INPUT:
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def quotient(self, sub, check=True): """ Return the quotient of ``self`` by the given sublattice ``sub``. INPUT:
def quotient(self, sub, check=True): """ Return the quotient of ``self`` by the given sublattice ``sub``. INPUT:
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def quotient(self, sub, check=True): """ Return the quotient of ``self`` by the given sublattice ``sub``. INPUT:
def quotient(self, sub, check=True): """ Return the quotient of ``self`` by the given sublattice ``sub``. INPUT:
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def span(self, *args, **kwds): """ Return the span of the given generators.
def span(self, *args, **kwds): """ Return the span of the given generators.
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def span(self, *args, **kwds): """ Return the span of the given generators.
def span(self, *args, **kwds): """ Return the span of the given generators.
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def span_of_basis(self, *args, **kwds): r""" Return the submodule with the given ``basis``.
def span_of_basis(self, *args, **kwds): r""" Return the submodule with the given ``basis``.
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def span_of_basis(self, *args, **kwds): r""" Return the submodule with the given ``basis``.
def span_of_basis(self, *args, **kwds): r""" Return the submodule with the given ``basis``.
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def _latex_(self): r""" Return a LaTeX representation of ``self``. OUTPUT:
def _latex_(self): r""" Return a LaTeX representation of ``self``. OUTPUT:
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def _repr_(self): r""" Return a string representation of ``self``.
def _repr_(self): r""" Return a string representation of ``self``.
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def _repr_(self): r""" Return a string representation of ``self``.
def _repr_(self): r""" Return a string representation of ``self``.
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def rank(self): r""" Return the rank of ``self``. OUTPUT: - integer. EXAMPLES:: sage: N = ToricLattice(3) sage: Ns = N.submodule([N(2,4,0), N(9,12,0)]) sage: Q = N/Ns sage: Q.rank() 1 sage: Ns = N.submodule([N(1,4,0)]) sage: Q = N/Ns sage: Q.rank() 2 """ return self.V().rank() - self.W().rank()
def rank(self): r""" Return the rank of ``self``. OUTPUT: Integer. The dimension of the free part of the quotient. EXAMPLES:: sage: N = ToricLattice(3) sage: Ns = N.submodule([N(2,4,0), N(9,12,0)]) sage: Q = N/Ns sage: Q.rank() 1 sage: Ns = N.submodule([N(1,4,0)]) sage: Q = N/Ns sage: Q.rank() 2 """ return self.V()...
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def quotient(self, sub, check=True): """ Return the quotient of ``self`` by the given sublattice ``sub``. INPUT:
def quotient(self, sub, check=True, positive_point=None, positive_dual_point=None): """ Return the quotient of ``self`` by the given sublattice ``sub``. INPUT:
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def quotient(self, sub, check=True): """ Return the quotient of ``self`` by the given sublattice ``sub``. INPUT:
def quotient(self, sub, check=True): """ Return the quotient of ``self`` by the given sublattice ``sub``. INPUT:
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def quotient(self, sub, check=True): """ Return the quotient of ``self`` by the given sublattice ``sub``. INPUT:
def quotient(self, sub, check=True): """ Return the quotient of ``self`` by the given sublattice ``sub``. INPUT:
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def span(self, *args, **kwds): """ Return the span of the given generators.
def span(self, *args, **kwds): """ Return the span of the given generators.
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def span(self, *args, **kwds): """ Return the span of the given generators.
def span(self, *args, **kwds): """ Return the span of the given generators.
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def span_of_basis(self, *args, **kwds): r""" Return the submodule with the given ``basis``.
def span_of_basis(self, *args, **kwds): r""" Return the submodule with the given ``basis``.
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def span_of_basis(self, *args, **kwds): r""" Return the submodule with the given ``basis``.
def span_of_basis(self, *args, **kwds): r""" Return the submodule with the given ``basis``.
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def _latex_(self): r""" Return a LaTeX representation of ``self``. OUTPUT:
def _latex_(self): r""" Return a LaTeX representation of ``self``. OUTPUT:
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def _repr_(self): r""" Return a string representation of ``self``.
def _repr_(self): r""" Return a string representation of ``self``.
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def _repr_(self): r""" Return a string representation of ``self``.
def _repr_(self): r""" Return a string representation of ``self``.
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def rank(self): r""" Return the rank of ``self``. OUTPUT: - integer. EXAMPLES:: sage: N = ToricLattice(3) sage: Ns = N.submodule([N(2,4,0), N(9,12,0)]) sage: Q = N/Ns sage: Q.rank() 1 sage: Ns = N.submodule([N(1,4,0)]) sage: Q = N/Ns sage: Q.rank() 2 """ return self.V().rank() - self.W().rank()
def rank(self): r""" Return the rank of ``self``. OUTPUT: Integer. The dimension of the free part of the quotient. EXAMPLES:: sage: N = ToricLattice(3) sage: Ns = N.submodule([N(2,4,0), N(9,12,0)]) sage: Q = N/Ns sage: Q.rank() 1 sage: Ns = N.submodule([N(1,4,0)]) sage: Q = N/Ns sage: Q.rank() 2 """ return self.V()...
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def uname_specific(name, value, alternative): if name in os.uname()[0]: return value else: return alternative
def uname_specific(name, value, alternative): if name in os.uname()[0]: return value else: return alternative
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def uname_specific(name, value, alternative): if name in os.uname()[0]: return value else: return alternative
def uname_specific(name, value, alternative): if name in os.uname()[0]: return value else: return alternative
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def uname_specific(name, value, alternative): if name in os.uname()[0]: return value else: return alternative
def uname_specific(name, value, alternative): if name in os.uname()[0]: return value else: return alternative
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def uname_specific(name, value, alternative): if name in os.uname()[0]: return value else: return alternative
def uname_specific(name, value, alternative): if name in os.uname()[0]: return value else: return alternative
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def __init__(self, maxread=10000, script_subdirectory=None, logfile=None, server=None, server_tmpdir=None, user_config=False): """ INPUT: - ``maxread`` - affects buffering - ``script_subdirectory`` - directory where scripts are read from - ``logfile`` - output logged to this file - ``server`` - address of remo...
def __init__(self, maxread=10000, script_subdirectory=None, logfile=None, server=None, server_tmpdir=None, user_config=False): """ INPUT: - ``maxread`` - affects buffering - ``script_subdirectory`` - directory where scripts are read from - ``logfile`` - output logged to this file - ``server`` - address of remo...
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def magma_console(): """ Run a command line Magma session. EXAMPLES:: sage: magma_console() # not tested Magma V2.14-9 Sat Oct 11 2008 06:36:41 on one [Seed = 1157408761] Type ? for help. Type <Ctrl>-D to quit. > Total time: 2.820 seconds, Total memory usage: 3.95MB """ console('magma')
def magma_console(): """ Run a command line Magma session. EXAMPLES:: sage: magma_console() # not tested Magma V2.14-9 Sat Oct 11 2008 06:36:41 on one [Seed = 1157408761] Type ? for help. Type <Ctrl>-D to quit. > Total time: 2.820 seconds, Total memory usage: 3.95MB """ console('sage-native-exec...
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def overlap_partition(self, other, delay=0, p=None, involution=None) : r""" Returns the partition of the alphabet induced by the overlap of self and other with the given delay.
def overlap_partition(self, other, delay=0, p=None, involution=None) : r""" Returns the partition of the alphabet induced by the overlap of self and other with the given delay.
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def __contains__(self, x): """ Returns True if x is contained in self.
def __contains__(self, x): """ Returns True if x is contained in self.
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def from_polynomial_exp(self, p): r""" Conversion from polynomial in exponential notation
def from_polynomial_exp(self, p): r""" Conversion from polynomial in exponential notation
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def __init__(self, *args, **kwargs): """ Construct a substitution box (S-box) for a given lookup table `S`.
def __init__(self, *args, **kwargs): """ Construct a substitution box (S-box) for a given lookup table `S`.
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def parse_deps(self, filename, verify=True): """ Open a Cython file and extract all of its dependencies. INPUT: filename -- the file to parse verify -- only return existing files (default True) OUTPUT: list of dependency files """ # only parse cython files if filename[-4:] not in ('.pyx', '.pxd', '.pxi'): return []...
def parse_deps(self, filename, ext_module, verify=True): """ Open a Cython file and extract all of its dependencies. INPUT: filename -- the file to parse verify -- only return existing files (default True) OUTPUT: list of dependency files """ # only parse cython files if filename[-4:] not in ('.pyx', '.pxd', '.pxi'...
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def parse_deps(self, filename, verify=True): """ Open a Cython file and extract all of its dependencies. INPUT: filename -- the file to parse verify -- only return existing files (default True) OUTPUT: list of dependency files """ # only parse cython files if filename[-4:] not in ('.pyx', '.pxd', '.pxi'): return []...
def parse_deps(self, filename, verify=True): """ Open a Cython file and extract all of its dependencies. INPUT: filename -- the file to parse verify -- only return existing files (default True) OUTPUT: list of dependency files """ # only parse cython files if not is_cython_file(filename): return [] dirname = os.pa...
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def parse_deps(self, filename, verify=True): """ Open a Cython file and extract all of its dependencies. INPUT: filename -- the file to parse verify -- only return existing files (default True) OUTPUT: list of dependency files """ # only parse cython files if filename[-4:] not in ('.pyx', '.pxd', '.pxi'): return []...
def parse_deps(self, filename, verify=True): """ Open a Cython file and extract all of its dependencies. INPUT: filename -- the file to parse verify -- only return existing files (default True) OUTPUT: list of dependency files """ # only parse cython files if filename[-4:] not in ('.pyx', '.pxd', '.pxi'): return []...
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def parse_deps(self, filename, verify=True): """ Open a Cython file and extract all of its dependencies. INPUT: filename -- the file to parse verify -- only return existing files (default True) OUTPUT: list of dependency files """ # only parse cython files if filename[-4:] not in ('.pyx', '.pxd', '.pxi'): return []...
def parse_deps(self, filename, verify=True): """ Open a Cython file and extract all of its dependencies. INPUT: filename -- the file to parse verify -- only return existing files (default True) OUTPUT: list of dependency files """ # only parse cython files if filename[-4:] not in ('.pyx', '.pxd', '.pxi'): return []...
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def immediate_deps(self, filename): """ Returns a list of files directly referenced by this file. """ if (filename not in self._deps or self.timestamp(filename) < self._last_parse[filename]): self._deps[filename] = self.parse_deps(filename) self._last_parse[filename] = self.timestamp(filename) return self._deps[filenam...
def immediate_deps(self, filename, ext_module): """ Returns a list of files directly referenced by this file. """ if (filename not in self._deps or self.timestamp(filename) < self._last_parse[filename]): self._deps[filename] = self.parse_deps(filename) self._last_parse[filename] = self.timestamp(filename) return self._...
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def immediate_deps(self, filename): """ Returns a list of files directly referenced by this file. """ if (filename not in self._deps or self.timestamp(filename) < self._last_parse[filename]): self._deps[filename] = self.parse_deps(filename) self._last_parse[filename] = self.timestamp(filename) return self._deps[filenam...
def immediate_deps(self, filename): """ Returns a list of files directly referenced by this file. """ if (filename not in self._deps or self.timestamp(filename) < self._last_parse[filename]): self._deps[filename] = self.parse_deps(filename, ext_module) self._last_parse[filename] = self.timestamp(filename) return self._...
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def all_deps(self, filename, path=None): """ Returns all files directly or indirectly referenced by this file. A recursive algorithm is used here to maximize caching, but it is still robust for circular cimports (via the path parameter). """ if filename not in self._deps_all: circular = False deps = set([filename]) if...
def all_deps(self, filename, ext_module, path=None): """ Returns all files directly or indirectly referenced by this file. A recursive algorithm is used here to maximize caching, but it is still robust for circular cimports (via the path parameter). """ if filename not in self._deps_all: circular = False deps = set([f...
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def all_deps(self, filename, path=None): """ Returns all files directly or indirectly referenced by this file. A recursive algorithm is used here to maximize caching, but it is still robust for circular cimports (via the path parameter). """ if filename not in self._deps_all: circular = False deps = set([filename]) if...
def all_deps(self, filename, path=None): """ Returns all files directly or indirectly referenced by this file. A recursive algorithm is used here to maximize caching, but it is still robust for circular cimports (via the path parameter). """ if filename not in self._deps_all: circular = False deps = set([filename]) if...
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def all_deps(self, filename, path=None): """ Returns all files directly or indirectly referenced by this file. A recursive algorithm is used here to maximize caching, but it is still robust for circular cimports (via the path parameter). """ if filename not in self._deps_all: circular = False deps = set([filename]) if...
def all_deps(self, filename, path=None): """ Returns all files directly or indirectly referenced by this file. A recursive algorithm is used here to maximize caching, but it is still robust for circular cimports (via the path parameter). """ if filename not in self._deps_all: circular = False deps = set([filename]) if...
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def newest_dep(self, filename): """ Returns the most recently modified file that filename depends on, along with its timestamp. """ nfile = filename ntime = self.timestamp(filename) for f in self.all_deps(filename): if self.timestamp(f) > ntime: nfile = f ntime = self.timestamp(f) return nfile, ntime
def newest_dep(self, filename, ext_module): """ Returns the most recently modified file that filename depends on, along with its timestamp. """ nfile = filename ntime = self.timestamp(filename) for f in self.all_deps(filename): if self.timestamp(f) > ntime: nfile = f ntime = self.timestamp(f) return nfile, ntime
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def newest_dep(self, filename): """ Returns the most recently modified file that filename depends on, along with its timestamp. """ nfile = filename ntime = self.timestamp(filename) for f in self.all_deps(filename): if self.timestamp(f) > ntime: nfile = f ntime = self.timestamp(f) return nfile, ntime
def newest_dep(self, filename): """ Returns the most recently modified file that filename depends on, along with its timestamp. """ nfile = filename ntime = self.timestamp(filename) for f in self.all_deps(filename, ext_module): if self.timestamp(f) > ntime: nfile = f ntime = self.timestamp(f) return nfile, ntime
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def compile_command_list(ext_modules, deps): """ Computes a list of commands needed to compile and link the extension modules given in 'ext_modules' """ queue_compile_high = [] queue_compile_med = [] queue_compile_low = [] for m in ext_modules: new_sources = [] for f in m.sources: if f.endswith('.pyx'): dep_file, dep_...
def compile_command_list(ext_modules, deps): """ Computes a list of commands needed to compile and link the extension modules given in 'ext_modules' """ queue_compile_high = [] queue_compile_med = [] queue_compile_low = [] for m in ext_modules: new_sources = [] for f in m.sources: if f.endswith('.pyx'): dep_file, dep_...
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def crt(a,b,m=None,n=None): r""" Returns a solution to a Chinese Remainder Theorem problem. INPUT: - ``a``, ``b`` - two residues (elements of some ring for which extended gcd is available), or two lists, one of residues and one of moduli. - ``m``, ``n`` - two moduli, or None. OUTPUT: If ``m``, ``n`` are not None, ...
def crt(a,b,m=None,n=None): r""" Returns a solution to a Chinese Remainder Theorem problem. INPUT: - ``a``, ``b`` - two residues (elements of some ring for which extended gcd is available), or two lists, one of residues and one of moduli. - ``m``, ``n`` - (default: ``None``) two moduli, or ``None``. OUTPUT: If ``m...
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def crt(a,b,m=None,n=None): r""" Returns a solution to a Chinese Remainder Theorem problem. INPUT: - ``a``, ``b`` - two residues (elements of some ring for which extended gcd is available), or two lists, one of residues and one of moduli. - ``m``, ``n`` - two moduli, or None. OUTPUT: If ``m``, ``n`` are not None, ...
def crt(a,b,m=None,n=None): r""" Returns a solution to a Chinese Remainder Theorem problem. INPUT: - ``a``, ``b`` - two residues (elements of some ring for which extended gcd is available), or two lists, one of residues and one of moduli. - ``m``, ``n`` - two moduli, or None. OUTPUT: If ``m``, ``n`` are not ``None...
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def crt(a,b,m=None,n=None): r""" Returns a solution to a Chinese Remainder Theorem problem. INPUT: - ``a``, ``b`` - two residues (elements of some ring for which extended gcd is available), or two lists, one of residues and one of moduli. - ``m``, ``n`` - two moduli, or None. OUTPUT: If ``m``, ``n`` are not None, ...
def crt(a,b,m=None,n=None): r""" Returns a solution to a Chinese Remainder Theorem problem. INPUT: - ``a``, ``b`` - two residues (elements of some ring for which extended gcd is available), or two lists, one of residues and one of moduli. - ``m``, ``n`` - two moduli, or None. OUTPUT: If ``m``, ``n`` are not None, ...
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def crt(a,b,m=None,n=None): r""" Returns a solution to a Chinese Remainder Theorem problem. INPUT: - ``a``, ``b`` - two residues (elements of some ring for which extended gcd is available), or two lists, one of residues and one of moduli. - ``m``, ``n`` - two moduli, or None. OUTPUT: If ``m``, ``n`` are not None, ...
def crt(a,b,m=None,n=None): r""" Returns a solution to a Chinese Remainder Theorem problem. INPUT: - ``a``, ``b`` - two residues (elements of some ring for which extended gcd is available), or two lists, one of residues and one of moduli. - ``m``, ``n`` - two moduli, or None. OUTPUT: If ``m``, ``n`` are not None, ...
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def crt(a,b,m=None,n=None): r""" Returns a solution to a Chinese Remainder Theorem problem. INPUT: - ``a``, ``b`` - two residues (elements of some ring for which extended gcd is available), or two lists, one of residues and one of moduli. - ``m``, ``n`` - two moduli, or None. OUTPUT: If ``m``, ``n`` are not None, ...
def crt(a,b,m=None,n=None): r""" Returns a solution to a Chinese Remainder Theorem problem. INPUT: - ``a``, ``b`` - two residues (elements of some ring for which extended gcd is available), or two lists, one of residues and one of moduli. - ``m``, ``n`` - two moduli, or None. OUTPUT: If ``m``, ``n`` are not None, ...
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def crt(a,b,m=None,n=None): r""" Returns a solution to a Chinese Remainder Theorem problem. INPUT: - ``a``, ``b`` - two residues (elements of some ring for which extended gcd is available), or two lists, one of residues and one of moduli. - ``m``, ``n`` - two moduli, or None. OUTPUT: If ``m``, ``n`` are not None, ...
def crt(a,b,m=None,n=None): r""" Returns a solution to a Chinese Remainder Theorem problem. INPUT: - ``a``, ``b`` - two residues (elements of some ring for which extended gcd is available), or two lists, one of residues and one of moduli. - ``m``, ``n`` - two moduli, or None. OUTPUT: If ``m``, ``n`` are not None, ...
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def update(self): """ Updates some properties from ``curve``.
def update(self): """ Updates some properties from ``curve``.
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sage: def foo(use_database):
sage: def foo(use_database):
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def __cmp__(self, other): r""" Define comparison for finite posets.
def __hash__(self): """ TESTS:: sage: P = Poset([[1,2],[3],[3]]) sage: P.__hash__() 6557284140853143473 584755121 sage: P = Poset([[1],[3],[3]]) sage: P.__hash__() 5699294501102840900 278031428 """ if self._hash is None: self._hash = tuple(map(tuple, self.cover_relations())).__hash__() return self._hash def __eq__(se...
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def __cmp__(self, other): r""" Define comparison for finite posets.
def __cmp__(self, other): r""" Define comparison for finite posets.
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def __cmp__(self, other): r""" Define comparison for finite posets.
def __cmp__(self, other): r""" Define comparison for finite posets.
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def __cmp__(self, other): r""" Define comparison for finite posets.
def __cmp__(self, other): r""" Define comparison for finite posets.
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def __cmp__(self, other): r""" Define comparison for finite posets.
def __cmp__(self, other): r""" Define comparison for finite posets.
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def __cmp__(self, other): r""" Define comparison for finite posets.
def __cmp__(self, other): r""" Define comparison for finite posets.
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def hasse_diagram(self): """ Returns the Hasse_diagram of the poset as a Sage DiGraph object. EXAMPLES:: sage: Q = Poset({5:[2,3], 1:[3,4], 2:[0], 3:[0], 4:[0]}) sage: Q.hasse_diagram() Digraph on 6 vertices
def hasse_diagram(self): """ Returns the Hasse_diagram of the poset as a Sage DiGraph object. EXAMPLES:: sage: Q = Poset({5:[2,3], 1:[3,4], 2:[0], 3:[0], 4:[0]}) sage: Q.hasse_diagram() Digraph on 6 vertices
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def is_Gamma0_equivalent(self, other, N, Transformation=False): r""" Checks if cusps ``self`` and ``other`` are `\Gamma_0(N)`- equivalent.
def is_Gamma0_equivalent(self, other, N, Transformation=False): r""" Checks if cusps ``self`` and ``other`` are `\Gamma_0(N)`- equivalent.
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def uname_specific(name, value, alternative): if name in os.uname()[0]: return value else: return alternative
def uname_specific(name, value, alternative): if name in os.uname()[0]: return value else: return alternative
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def _repr_defn(self): """ This function is used internally for printing.
def _repr_defn(self): """ This function is used internally for printing.
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def __init__(self, parent, polys, check=True): SchemeMorphism_on_points.__init__(self, parent, polys, check) if check: # morphisms from projective space are always given by # homogeneous polynomials of the same degree deg = self.defining_polynomials()[0].degree() for poly in self.defining_polynomials(): if (poly.degree...
def __init__(self, parent, polys, check=True): SchemeMorphism_on_points.__init__(self, parent, polys, check) if check: # morphisms from projective space are always given by # homogeneous polynomials of the same degree polys = self.defining_polynomials() try: d = polys[0].degree() except AttributeError: polys = [f.lift(...
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def _eval_(self, x): """ EXAMPLES::
def _eval_(self, x): """ EXAMPLES::
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def _eval_(self, x): """ EXAMPLES::
def _eval_(self, x): """ EXAMPLES::
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def _eval_(self, x): """ EXAMPLES::
def _eval_(self, x): """ EXAMPLES::
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'@square...def g(x)...'
'@square...def g(x)...'
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def _call_(self, x): """ Construct a module with basis from the data in ``x``
def _call_(self, x): """ Construct a module with basis from the data in ``x``
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def is_abelian(self): """ Returns whether this category is abelian
def is_abelian(self): """ Returns whether this category is abelian
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def module_morphism(self, on_basis = None, diagonal = None, triangular = None, **keywords): r""" Constructs morphisms by linearity
def module_morphism(self, on_basis = None, diagonal = None, triangular = None, **keywords): r""" Constructs morphisms by linearity
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def module_morphism(self, on_basis = None, diagonal = None, triangular = None, **keywords): r""" Constructs morphisms by linearity
def module_morphism(self, on_basis = None, diagonal = None, triangular = None, **keywords): r""" Constructs morphisms by linearity
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def log(x, base=None): """ Return the logarithm of x to the given base. Calls the ``log`` method of the object x when computing the logarithm, thus allowing use of logarithm on any object containing a ``log`` method. In other words, log works on more than just real numbers. EXAMPLES:: sage: log(e^2) 2 sage: log(1024...
def log(x, base=None): """ Return the logarithm of x to the given base. Calls the ``log`` method of the object x when computing the logarithm, thus allowing use of logarithm on any object containing a ``log`` method. In other words, log works on more than just real numbers. EXAMPLES:: sage: log(e^2) 2 sage: log(1024...
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def log(x, base=None): """ Return the logarithm of x to the given base. Calls the ``log`` method of the object x when computing the logarithm, thus allowing use of logarithm on any object containing a ``log`` method. In other words, log works on more than just real numbers. EXAMPLES:: sage: log(e^2) 2 sage: log(1024...
def log(x, base=None): """ Return the logarithm of x to the given base. Calls the ``log`` method of the object x when computing the logarithm, thus allowing use of logarithm on any object containing a ``log`` method. In other words, log works on more than just real numbers. EXAMPLES:: sage: log(e^2) 2 sage: log(1024...
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def _sympy_(self): """ Converts pi to sympy pi. EXAMPLES:: sage: import sympy sage: sympy.pi == pi # indirect doctest True """ import sympy return sympy.pi
def _sympy_(self): """ Converts pi to sympy pi. EXAMPLES:: sage: import sympy sage: sympy.pi == pi # indirect doctest True """ import sympy return sympy.pi
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def sturm_bound(self, M=None): r""" For a space M of modular forms, this function returns an integer B such that two modular forms in either self or M are equal if and only if their q-expansions are equal to precision B (note that this is 1+ the usual Sturm bound, since `O(q^\mathrm{prec})` has precision prec). If M is...
def sturm_bound(self, M=None): r""" For a space M of modular forms, this function returns an integer B such that two modular forms in either self or M are equal if and only if their q-expansions are equal to precision B (note that this is 1+ the usual Sturm bound, since `O(q^\mathrm{prec})` has precision prec). If M is...
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def _subdivide_palp(self, new_rays, verbose): r""" Subdivide ``self`` adding ``new_rays`` one by one.
def _subdivide_palp(self, new_rays, verbose): r""" Subdivide ``self`` adding ``new_rays`` one by one.
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def _subdivide_palp(self, new_rays, verbose): r""" Subdivide ``self`` adding ``new_rays`` one by one.
def _subdivide_palp(self, new_rays, verbose): r""" Subdivide ``self`` adding ``new_rays`` one by one.
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def is_cyclic_ordered(x1,x2,x3): return ( (x1 < x2 and x2 < x3) or (x2 < x3 and x3 < x1) or (x3 < x1 and x1 < x2))
def is_cyclic_ordered(x1,x2,x3): return ( (x1 < x2 and x2 < x3) or (x2 < x3 and x3 < x1) or (x3 < x1 and x1 < x2))
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def is_cyclic_ordered(x1,x2,x3): return ( (x1 < x2 and x2 < x3) or (x2 < x3 and x3 < x1) or (x3 < x1 and x1 < x2))
def is_cyclic_ordered(x1,x2,x3): return ( (x1 < x2 and x2 < x3) or (x2 < x3 and x3 < x1) or (x3 < x1 and x1 < x2))
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def is_cyclic_ordered(x1,x2,x3): return ( (x1 < x2 and x2 < x3) or (x2 < x3 and x3 < x1) or (x3 < x1 and x1 < x2))
def is_cyclic_ordered(x1,x2,x3): return ( (x1 < x2 and x2 < x3) or (x2 < x3 and x3 < x1) or (x3 < x1 and x1 < x2))
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def __init__(self, x, y, r1, r2, angle, s1, s2, options): """ Initializes base class Arc.
def __init__(self, x, y, r1, r2, angle, s1, s2, options): """ Initializes base class Arc.
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def get_minmax_data(self): """ Returns a dictionary with the bounding box data.
def get_minmax_data(self): """ Returns a dictionary with the bounding box data.
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