bugged
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4
228k
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96.3M
__index_level_0__
int64
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def __classcall_private__(cls,p): r""" This function tries to recognize the input (it can be either a list or a tuple of pairs, or a fix-point free involution given as a list or as a permutation), constructs the parent (enumerated set of PerfectMatchings of the ground set) and calls the __init__ function to construct o...
def __classcall_private__(cls,p): r""" This function tries to recognize the input (it can be either a list or a tuple of pairs, or a fix-point free involution given as a list or as a permutation), constructs the parent (enumerated set of PerfectMatchings of the ground set) and calls the __init__ function to construct o...
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def __classcall_private__(cls,p): r""" This function tries to recognize the input (it can be either a list or a tuple of pairs, or a fix-point free involution given as a list or as a permutation), constructs the parent (enumerated set of PerfectMatchings of the ground set) and calls the __init__ function to construct o...
def __classcall_private__(cls,p): r""" This function tries to recognize the input (it can be either a list or a tuple of pairs, or a fix-point free involution given as a list or as a permutation), constructs the parent (enumerated set of PerfectMatchings of the ground set) and calls the __init__ function to construct o...
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def __classcall_private__(cls,p): r""" This function tries to recognize the input (it can be either a list or a tuple of pairs, or a fix-point free involution given as a list or as a permutation), constructs the parent (enumerated set of PerfectMatchings of the ground set) and calls the __init__ function to construct o...
def __classcall_private__(cls,p): r""" This function tries to recognize the input (it can be either a list or a tuple of pairs, or a fix-point free involution given as a list or as a permutation), constructs the parent (enumerated set of PerfectMatchings of the ground set) and calls the __init__ function to construct o...
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def trial_division(n, bound=None): """ Return the smallest prime divisor <= bound of the positive integer n, or n if there is no such prime. If the optional argument bound is omitted, then bound <= n. INPUT: - ``n`` - a positive integer - ``bound`` - (optional) a positive integer OUTPUT: - ``int`` - a prime p=bo...
def trial_division(n, bound=None): """ Return the smallest prime divisor <= bound of the positive integer n, or n if there is no such prime. If the optional argument bound is omitted, then bound <= n. INPUT: - ``n`` - a positive integer - ``bound`` - (optional) a positive integer OUTPUT: - ``int`` - a prime p=bo...
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def factor(n, proof=None, int_=False, algorithm='pari', verbose=0, **kwds): """ Returns the factorization of n. The result depends on the type of n. If n is an integer, factor returns the factorization of the integer n as an object of type Factorization. If n is not an integer, ``n.factor(proof=proof, **kwds)`` gets ...
def if n < 10000000000000: return factorization.Factorization(__factor_using_trial_division(n), unit) factor(n, if n < 10000000000000: return factorization.Factorization(__factor_using_trial_division(n), unit) proof=None, if n < 10000000000000: return factorization.Factorization(__factor_using_trial_division(n), unit...
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def is_identity(self): r""" Returns ``True`` if ``self`` is the identity morphism.
def is_identity(self): r""" Returns ``True`` if ``self`` is the identity morphism.
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def is_homogeneous(self, polynomial): r""" Check if ``polynomial`` is homogeneous.
def is_homogeneous(self, polynomial): r""" Check if ``polynomial`` is homogeneous.
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def is_homogeneous(self, polynomial): r""" Check if ``polynomial`` is homogeneous.
def is_homogeneous(self, polynomial): r""" Check if ``polynomial`` is homogeneous.
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def intermediate_shape(self): """ Returns the intermediate shape of the pm diagram (innner shape plus positions of plusses)
def intermediate_shape(self): """ Returns the intermediate shape of the pm diagram (innner shape plus positions of plusses)
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def intermediate_shape(self): """ Returns the intermediate shape of the pm diagram (innner shape plus positions of plusses)
def intermediate_shape(self): """ Returns the intermediate shape of the pm diagram (innner shape plus positions of plusses)
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def blocks_and_cut_vertices(self): """ Computes the blocks and cut vertices of the graph. In the case of a digraph, this computation is done on the underlying graph.
def blocks_and_cut_vertices(self): """ Computes the blocks and cut vertices of the graph. In the case of a digraph, this computation is done on the underlying graph.
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def blocks_and_cut_vertices(self): """ Computes the blocks and cut vertices of the graph. In the case of a digraph, this computation is done on the underlying graph.
def blocks_and_cut_vertices(self): """ Computes the blocks and cut vertices of the graph. In the case of a digraph, this computation is done on the underlying graph.
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def face_lattice(self): """ Computes the face-lattice poset. Elements are tuples of (vertices, facets) - i.e. this keeps track of both the vertices in each face, and all the facets containing them.
def face_lattice(self): """ Computes the face-lattice poset. Elements are tuples of (vertices, facets) - i.e. this keeps track of both the vertices in each face, and all the facets containing them.
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def face_lattice(self): """ Computes the face-lattice poset. Elements are tuples of (vertices, facets) - i.e. this keeps track of both the vertices in each face, and all the facets containing them.
def face_lattice(self): """ Computes the face-lattice poset. Elements are tuples of (vertices, facets) - i.e. this keeps track of both the vertices in each face, and all the facets containing them.
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def matching_polynomial(self, complement=True, name=None): """ Computes the matching polynomial of the graph G.
def matching_polynomial(self, complement=True, name=None): """ Computes the matching polynomial of the graph G.
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def matching_polynomial(self, complement=True, name=None): """ Computes the matching polynomial of the graph G.
def matching_polynomial(self, complement=True, name=None): """ Computes the matching polynomial of the graph G.
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def matching_polynomial(self, complement=True, name=None): """ Computes the matching polynomial of the graph G.
def matching_polynomial(self, complement=True, name=None): """ Computes the matching polynomial of the graph G.
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def _repr_(self): """ The printing representation of self.
def _repr_(self): """ The printing representation of self.
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def _repr_(self): """ The default printing representation of self.
def _repr_(self): """ The default printing representation of self.
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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 leading_item(self, cmp=None): r""" Returns the pair ``(k, c)`` where ``c`` * (the basis elt. indexed by ``k``) is the leading term of ``self``.
def leading_item(self, cmp=None): r""" Returns the pair ``(k, c)`` where ``c`` * (the basis elt. indexed by ``k``) is the leading term of ``self``.
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def leading_monomial(self, cmp=None): r""" Returns the leading monomial of ``self``.
def leading_monomial(self, cmp=None): r""" Returns the leading monomial of ``self``.
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def leading_coefficient(self, cmp=None): r""" Returns the leading coefficient of ``self``.
def leading_coefficient(self, cmp=None): r""" Returns the leading coefficient of ``self``.
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def leading_term(self, cmp=None): r""" Returns the leading term of ``self``.
def leading_term(self, cmp=None): r""" Returns the leading term of ``self``.
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def trailing_item(self, cmp=None): r""" Returns the pair ``(c, k)`` where ``c*self.parent().monomial(k)`` is the trailing term of ``self``.
def trailing_item(self, cmp=None): r""" Returns the pair ``(c, k)`` where ``c*self.parent().monomial(k)`` is the trailing term of ``self``.
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def trailing_monomial(self, cmp=None): r""" Returns the trailing monomial of ``self``.
def trailing_monomial(self, cmp=None): r""" Returns the trailing monomial of ``self``.
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def trailing_coefficient(self, cmp=None): r""" Returns the trailing coefficient of ``self``.
def trailing_coefficient(self, cmp=None): r""" Returns the trailing coefficient of ``self``.
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def trailing_term(self, cmp=None): r""" Returns the trailing term of ``self``.
def trailing_term(self, cmp=None): r""" Returns the trailing term of ``self``.
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def extra_super_categories(self): """ EXAMPLES::
def extra_super_categories(self): """ EXAMPLES::
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sage: def phi_on_basis(i): return Y.monomial(abs(i))
sage: def phi_on_basis(i): return Y.monomial(abs(i))
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sage: def phi_on_basis(i): return Y.monomial(abs(i))
sage: def phi_on_basis(i): return Y.monomial(abs(i))
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sage: def phi_on_basis(i): return Y.monomial(abs(i))
sage: def phi_on_basis(i): return Y.monomial(abs(i))
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def _test_triangular(self, **options): """ Tests that ``self`` is actually triangular
def _test_triangular(self, **options): """ Tests that ``self`` is actually triangular
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def _test_triangular(self, **options): """ Tests that ``self`` is actually triangular
def _test_triangular(self, **options): """ Tests that ``self`` is actually triangular
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def _test_triangular(self, **options): """ Tests that ``self`` is actually triangular
def _test_triangular(self, **options): """ Tests that ``self`` is actually triangular
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def _test_triangular(self, **options): """ Tests that ``self`` is actually triangular
def _test_triangular(self, **options): """ Tests that ``self`` is actually triangular
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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 hasse_invariant(self): r""" Returns the Hasse invariant of an elliptic curve over a field of positive characteristic, which is an element of the field.
def hasse_invariant(self): r""" Returns the Hasse invariant of an elliptic curve over a field of positive characteristic, which is an element of the field.
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def hasse_invariant(self): r""" Returns the Hasse invariant of an elliptic curve over a field of positive characteristic, which is an element of the field.
def hasse_invariant(self): r""" Returns the Hasse invariant of an elliptic curve over a field of positive characteristic, which is an element of the field.
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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 parse_deps(self, filename, verify=True): """ Open a Cython file and extract all of its dependencies.
def parse_deps(self, filename, ext_module, verify=True): """ Open a Cython file and extract all of its dependencies.
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def parse_deps(self, filename, verify=True): """ Open a Cython file and extract all of its dependencies.
def parse_deps(self, filename, verify=True): """ Open a Cython file and extract all of its dependencies.
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def parse_deps(self, filename, verify=True): """ Open a Cython file and extract all of its dependencies.
def parse_deps(self, filename, verify=True): """ Open a Cython file and extract all of its dependencies.
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def parse_deps(self, filename, verify=True): """ Open a Cython file and extract all of its dependencies.
def parse_deps(self, filename, verify=True): """ Open a Cython file and extract all of its dependencies.
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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.
def all_deps(self, filename, ext_module, path=None): """ Returns all files directly or indirectly referenced by this file.
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def all_deps(self, filename, path=None): """ Returns all files directly or indirectly referenced by this file.
def all_deps(self, filename, path=None): """ Returns all files directly or indirectly referenced by this file.
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def all_deps(self, filename, path=None): """ Returns all files directly or indirectly referenced by this file.
def all_deps(self, filename, path=None): """ Returns all files directly or indirectly referenced by this file.
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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 show(self, **kwds): """ Show this graphics image with the default image viewer.
def show(self, **kwds): """ Show this graphics image with the default image viewer.
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def derivative(self, ex, operator): """ EXAMPLES::
def derivative(self, ex, operator): """ EXAMPLES::
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def derivative(self, ex, operator): """ EXAMPLES::
def derivative(self, ex, operator): """ EXAMPLES::
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def derivative(self, ex, operator): """ EXAMPLES::
def derivative(self, ex, operator): """ EXAMPLES::
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def derivative(self, ex, operator): """ EXAMPLES::
def derivative(self, ex, operator): """ EXAMPLES::
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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 enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E...
def enum_projective_rational_field(X,B): r""" Enumerates projective, rational points on scheme ``X`` of height up to bound ``B``. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, s...
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def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E...
def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme; - ``B`` - a positive integer bound. OUTPUT: - a list containing the projective points of X of height up to B, sorted. ...
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def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E...
def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of ``X`` of height up to ``B``, so...
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def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E...
def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E...
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def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E...
def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E...
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def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E...
def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E...
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def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E...
def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E...
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def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E...
def enum_projective_rational_field(X,B): """ Enumerates projective, rational points on scheme X of height up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme. - ``B`` - a positive integer bound OUTPUT: - a list containing the projective points of X of height up to B, sorted. E...
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def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM...
def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme ``X`` (defined over `\QQ`) up to bound ``B``. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorte...
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def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM...
def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme; - ``B`` - a positive integer bound. OUTPUT: - a list containing the affine points of X of height up to B, sorted. EX...
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def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM...
def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of ``X`` of height up to ``B``, sorte...
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def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM...
def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM...
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def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM...
def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM...
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def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM...
def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM...
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def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM...
def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM...
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def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM...
def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM...
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def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM...
def enum_affine_rational_field(X,B): """ Enumerates affine rational points on scheme X (defined over `\QQ`) up to bound B. INPUT: - ``X`` - a scheme or set of abstract rational points of a scheme - ``B`` - a positive integer bound OUTPUT: - a list containing the affine points of X of height up to B, sorted. EXAM...
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def enum_projective_finite_field(X): """ Enumerates projective points on scheme X defined over a finite field INPUT: - ``X`` - a scheme defined over a finite field or set of abstract rational points of such a scheme OUTPUT: - a list containing the projective points of X over the finite field, sorted EXAMPLES:: s...
def enum_projective_finite_field(X): """ Enumerates projective points on scheme ``X`` defined over a finite field. INPUT: - ``X`` - a scheme defined over a finite field or set of abstract rational points of such a scheme OUTPUT: - a list containing the projective points of X over the finite field, sorted EXAMPLES...
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def enum_projective_finite_field(X): """ Enumerates projective points on scheme X defined over a finite field INPUT: - ``X`` - a scheme defined over a finite field or set of abstract rational points of such a scheme OUTPUT: - a list containing the projective points of X over the finite field, sorted EXAMPLES:: s...
def enum_projective_finite_field(X): """ Enumerates projective points on scheme X defined over a finite field INPUT: - ``X`` - a scheme defined over a finite field or a set of abstract rational points of such a scheme. OUTPUT: - a list containing the projective points of X over the finite field, sorted EXAMPLES::...
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def enum_projective_finite_field(X): """ Enumerates projective points on scheme X defined over a finite field INPUT: - ``X`` - a scheme defined over a finite field or set of abstract rational points of such a scheme OUTPUT: - a list containing the projective points of X over the finite field, sorted EXAMPLES:: s...
def enum_projective_finite_field(X): """ Enumerates projective points on scheme X defined over a finite field INPUT: - ``X`` - a scheme defined over a finite field or set of abstract rational points of such a scheme OUTPUT: - a list containing the projective points of ``X`` over the finite field, sorted. EXAMPLES...
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def enum_projective_finite_field(X): """ Enumerates projective points on scheme X defined over a finite field INPUT: - ``X`` - a scheme defined over a finite field or set of abstract rational points of such a scheme OUTPUT: - a list containing the projective points of X over the finite field, sorted EXAMPLES:: s...
def enum_projective_finite_field(X): """ Enumerates projective points on scheme X defined over a finite field INPUT: - ``X`` - a scheme defined over a finite field or set of abstract rational points of such a scheme OUTPUT: - a list containing the projective points of X over the finite field, sorted EXAMPLES:: s...
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def enum_projective_finite_field(X): """ Enumerates projective points on scheme X defined over a finite field INPUT: - ``X`` - a scheme defined over a finite field or set of abstract rational points of such a scheme OUTPUT: - a list containing the projective points of X over the finite field, sorted EXAMPLES:: s...
def enum_projective_finite_field(X): """ Enumerates projective points on scheme X defined over a finite field INPUT: - ``X`` - a scheme defined over a finite field or set of abstract rational points of such a scheme OUTPUT: - a list containing the projective points of X over the finite field, sorted EXAMPLES:: s...
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def identity_matrix(ring, n=0, sparse=False): r""" Return the `n \times n` identity matrix over the given ring. The default ring is the integers. EXAMPLES:: sage: M = identity_matrix(QQ, 2); M [1 0] [0 1] sage: M.parent() Full MatrixSpace of 2 by 2 dense matrices over Rational Field sage: M = identity_matrix(2); M [...
def identity_matrix(ring, n=0, sparse=False): r""" Return the `n \times n` identity matrix over the given ring. The default ring is the integers. EXAMPLES:: sage: M = identity_matrix(QQ, 2); M [1 0] [0 1] sage: M.parent() Full MatrixSpace of 2 by 2 dense matrices over Rational Field sage: M = identity_matrix(2); M [...
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def zero_matrix(ring, nrows, ncols=None, sparse=False): r""" Return the `nrows \times ncols` zero matrix over the given ring. The default ring is the integers. EXAMPLES:: sage: M = zero_matrix(QQ, 2); M [0 0] [0 0] sage: M.parent() Full MatrixSpace of 2 by 2 dense matrices over Rational Field sage: M = zero_matrix(2...
def zero_matrix(ring, nrows, ncols=None, sparse=False): r""" Return the `nrows \times ncols` zero matrix over the given ring. The default ring is the integers. EXAMPLES:: sage: M = zero_matrix(QQ, 2); M [0 0] [0 0] sage: M.parent() Full MatrixSpace of 2 by 2 dense matrices over Rational Field sage: M = zero_matrix(2...
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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 deg = self.defining_polynomials()[0].degree() for poly in self.defining_polynomials(): if (poly.degree...
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def edge_coloring(g, value_only=False, vizing=False, hex_colors=False, log=0): r""" Properly colors the edges of a graph. See the URL http://en.wikipedia.org/wiki/Edge_coloring for further details on edge coloring. INPUT: - ``g`` -- a graph. - ``value_only`` -- (default: ``False``): - When set to ``True``, only the...
def edge_coloring(g, value_only=False, vizing=False, hex_colors=False, log=0): r""" Properly colors the edges of a graph. See the URL http://en.wikipedia.org/wiki/Edge_coloring for further details on edge coloring. INPUT: - ``g`` -- a graph. - ``value_only`` -- (default: ``False``): - When set to ``True``, only the...
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def minpoly(ex, var='x', algorithm=None, bits=None, degree=None, epsilon=0): r""" Return the minimal polynomial of self, if possible. INPUT: - ``var`` - polynomial variable name (default 'x') - ``algorithm`` - 'algebraic' or 'numerical' (default both, but with numerical first) - ``bits`` - the number of bits to ...
def minpoly(ex, var='x', algorithm=None, bits=None, degree=None, epsilon=0): r""" Return the minimal polynomial of self, if possible. INPUT: - ``var`` - polynomial variable name (default 'x') - ``algorithm`` - 'algebraic' or 'numerical' (default both, but with numerical first) - ``bits`` - the number of bits to ...
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def _limit_latex_(self, f, x, a): r""" Return latex expression for limit of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _limit_latex_ sage: var('x,a') (x, a) sage: f = function('f',x) sage: _limit_latex_(0, f, x, a) '\\lim_{x \\to a}\\, f\\left(x\\right)' sage: latex(limit(f, x=oo)) \lim_...
def _limit_latex_(self, f, x, a): r""" Return latex expression for limit of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _limit_latex_ sage: var('x,a') (x, a) sage: f = function('f',x) sage: _limit_latex_(0, f, x, a) '\\lim_{x \\to a}\\, f\\left(x\\right)' sage: latex(limit(f, x=oo)) \lim_...
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def _laplace_latex_(self, *args): r""" Return LaTeX expression for Laplace transform of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _laplace_latex_ sage: var('s,t') (s, t) sage: f = function('f',t) sage: _laplace_latex_(0,f,t,s) '\\mathcal{L}\\left(f\\left(t\\right), t, s\\right)' sage: l...
def _laplace_latex_(self, *args): r""" Return LaTeX expression for Laplace transform of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _laplace_latex_ sage: var('s,t') (s, t) sage: f = function('f',t) sage: _laplace_latex_(0,f,t,s) '\\mathcal{L}\\left(f\\left(t\\right), t, s\\right)' sage: l...
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def _inverse_laplace_latex_(self, *args): r""" Return LaTeX expression for inverse Laplace transform of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _inverse_laplace_latex_ sage: var('s,t') (s, t) sage: F = function('F',s) sage: _inverse_laplace_latex_(0,F,s,t) '\\mathcal{L}^{-1}\\left(F\\...
def _inverse_laplace_latex_(self, *args): r""" Return LaTeX expression for inverse Laplace transform of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _inverse_laplace_latex_ sage: var('s,t') (s, t) sage: F = function('F',s) sage: _inverse_laplace_latex_(0,F,s,t) '\\mathcal{L}^{-1}\\left(F\\...
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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 frequency_table(string): r""" Return the frequency table corresponding to the given string. INPUT: - ``string`` -- a string EXAMPLE:: sage: from sage.coding.source_coding.huffman import frequency_table sage: str = "Sage is my most favorite general purpose computer algebra system" sage: frequency_table(str) {'a'...
def frequency_table(string): r""" Return the frequency table corresponding to the given string. INPUT: - ``string`` -- a string EXAMPLE:: sage: from sage.coding.source_coding.huffman import frequency_table sage: str = "Sage is my most favorite general purpose computer algebra system" sage: frequency_table(str) {'a'...
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def frequency_table(string): r""" Return the frequency table corresponding to the given string. INPUT: - ``string`` -- a string EXAMPLE:: sage: from sage.coding.source_coding.huffman import frequency_table sage: str = "Sage is my most favorite general purpose computer algebra system" sage: frequency_table(str) {'a'...
def frequency_table(string): r""" Return the frequency table corresponding to the given string. INPUT: - ``string`` -- a string of symbols over some alphabet. OUTPUT: - A table of frequency of each unique symbol in ``string``. If ``string`` is an empty string, return an empty table. EXAMPLES: The frequency table ...
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def frequency_table(string): r""" Return the frequency table corresponding to the given string. INPUT: - ``string`` -- a string EXAMPLE:: sage: from sage.coding.source_coding.huffman import frequency_table sage: str = "Sage is my most favorite general purpose computer algebra system" sage: frequency_table(str) {'a'...
def frequency_table(string): r""" Return the frequency table corresponding to the given string. INPUT: - ``string`` -- a string EXAMPLE:: sage: from sage.coding.source_coding.huffman import frequency_table sage: str = "Stop counting my characters!" sage: T = sorted(frequency_table(str).items()) sage: for symbol, co...
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def frequency_table(string): r""" Return the frequency table corresponding to the given string. INPUT: - ``string`` -- a string EXAMPLE:: sage: from sage.coding.source_coding.huffman import frequency_table sage: str = "Sage is my most favorite general purpose computer algebra system" sage: frequency_table(str) {'a'...
def frequency_table(string): r""" Return the frequency table corresponding to the given string. INPUT: - ``string`` -- a string EXAMPLE:: sage: from sage.coding.source_coding.huffman import frequency_table sage: str = "Sage is my most favorite general purpose computer algebra system" sage: frequency_table(str) {'a'...
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def frequency_table(string): r""" Return the frequency table corresponding to the given string. INPUT: - ``string`` -- a string EXAMPLE:: sage: from sage.coding.source_coding.huffman import frequency_table sage: str = "Sage is my most favorite general purpose computer algebra system" sage: frequency_table(str) {'a'...
def frequency_table(string): r""" Return the frequency table corresponding to the given string. INPUT: - ``string`` -- a string EXAMPLE:: sage: from sage.coding.source_coding.huffman import frequency_table sage: str = "Sage is my most favorite general purpose computer algebra system" sage: frequency_table(str) {'a'...
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def frequency_table(string): r""" Return the frequency table corresponding to the given string. INPUT: - ``string`` -- a string EXAMPLE:: sage: from sage.coding.source_coding.huffman import frequency_table sage: str = "Sage is my most favorite general purpose computer algebra system" sage: frequency_table(str) {'a'...
def frequency_table(string): r""" Return the frequency table corresponding to the given string. INPUT: - ``string`` -- a string EXAMPLE:: sage: from sage.coding.source_coding.huffman import frequency_table sage: str = "Sage is my most favorite general purpose computer algebra system" sage: frequency_table(str) {'a'...
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def frequency_table(string): r""" Return the frequency table corresponding to the given string. INPUT: - ``string`` -- a string EXAMPLE:: sage: from sage.coding.source_coding.huffman import frequency_table sage: str = "Sage is my most favorite general purpose computer algebra system" sage: frequency_table(str) {'a'...
def frequency_table(string): r""" Return the frequency table corresponding to the given string. INPUT: - ``string`` -- a string EXAMPLE:: sage: from sage.coding.source_coding.huffman import frequency_table sage: str = "Sage is my most favorite general purpose computer algebra system" sage: frequency_table(str) {'a'...
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def frequency_table(string): r""" Return the frequency table corresponding to the given string. INPUT: - ``string`` -- a string EXAMPLE:: sage: from sage.coding.source_coding.huffman import frequency_table sage: str = "Sage is my most favorite general purpose computer algebra system" sage: frequency_table(str) {'a'...
def frequency_table(string): r""" Return the frequency table corresponding to the given string. INPUT: - ``string`` -- a string EXAMPLE:: sage: from sage.coding.source_coding.huffman import frequency_table sage: str = "Sage is my most favorite general purpose computer algebra system" sage: frequency_table(str) {'a'...
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def frequency_table(string): r""" Return the frequency table corresponding to the given string. INPUT: - ``string`` -- a string EXAMPLE:: sage: from sage.coding.source_coding.huffman import frequency_table sage: str = "Sage is my most favorite general purpose computer algebra system" sage: frequency_table(str) {'a'...
def frequency_table(string): r""" Return the frequency table corresponding to the given string. INPUT: - ``string`` -- a string EXAMPLE:: sage: from sage.coding.source_coding.huffman import frequency_table sage: str = "Sage is my most favorite general purpose computer algebra system" sage: frequency_table(str) {'a'...
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