bugged stringlengths 4 228k | fixed stringlengths 0 96.3M | __index_level_0__ int64 0 481k |
|---|---|---|
def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. INPUT: - extend (True) decides if base field extensions should be considered or not. OUTPUT: A sequence of tuples. Each tuple contains an eigenvalue, a list with a basis of the corresponding subspace of eigenvectors... | def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. INPUT: - extend (True) decides if base field extensions should be considered or not. OUTPUT: A sequence of tuples. Each tuple contains an eigenvalue, a list with a basis of the corresponding subspace of eigenvectors... | 461,700 |
def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. INPUT: - extend (True) decides if base field extensions should be considered or not. OUTPUT: A sequence of tuples. Each tuple contains an eigenvalue, a list with a basis of the corresponding subspace of eigenvectors... | def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. INPUT: - extend (True) decides if base field extensions should be considered or not. OUTPUT: A sequence of tuples. Each tuple contains an eigenvalue, a list with a basis of the corresponding subspace of eigenvectors... | 461,701 |
def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. INPUT: - extend (True) decides if base field extensions should be considered or not. OUTPUT: A sequence of tuples. Each tuple contains an eigenvalue, a list with a basis of the corresponding subspace of eigenvectors... | def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. INPUT: - extend (True) decides if base field extensions should be considered or not. OUTPUT: A sequence of tuples. Each tuple contains an eigenvalue, a list with a basis of the corresponding subspace of eigenvectors... | 461,702 |
def minpoly(self,var='x'): """ Computes the minimal polynomial. INPUT: - ``var`` - string (default: 'x') a variable OUTPUT: polynomial in var - the minimal polynomial of the endomorphism. EXAMPLES: Compute the minimal polynomial, and check it :: sage: V=GF(7)^3 sage: H=V.Hom(V)([[0,1,2],[-1,0,3],[2,4,1]]) sage:... | def minpoly(self,var='x'): """ Computes the minimal polynomial. INPUT: - ``var`` - string (default: 'x') a variable name OUTPUT: polynomial in var - the minimal polynomial of the endomorphism. EXAMPLES: Compute the minimal polynomial, and check it :: sage: V=GF(7)^3 sage: H=V.Hom(V)([[0,1,2],[-1,0,3],[2,4,1]]) ... | 461,703 |
def minpoly(self,var='x'): """ Computes the minimal polynomial. INPUT: - ``var`` - string (default: 'x') a variable OUTPUT: polynomial in var - the minimal polynomial of the endomorphism. EXAMPLES: Compute the minimal polynomial, and check it :: sage: V=GF(7)^3 sage: H=V.Hom(V)([[0,1,2],[-1,0,3],[2,4,1]]) sage:... | def minpoly(self,var='x'): """ Computes the minimal polynomial. INPUT: - ``var`` - string (default: 'x') a variable OUTPUT: polynomial in var - the minimal polynomial of the endomorphism. EXAMPLES: Compute the minimal polynomial, and check it :: sage: V=GF(7)^3 sage: H=V.Hom(V)([[0,1,2],[-1,0,3],[2,4,1]]) sage:... | 461,704 |
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... | 461,705 |
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... | 461,706 |
def __cmp__(self, right): r""" Compare ``self`` and ``right``. | def __cmp__(self, right): r""" Compare ``self`` and ``right``. | 461,707 |
def is_square_free(self): r""" Returns True if self does not contain squares, and False otherwise. EXAMPLES:: sage: W = Words('123') sage: W('12312').is_square_free() True sage: W('31212').is_square_free() False sage: W().is_square_free() True """ l = self.length() if l < 2: return True suff = self for i in xrange(0,... | def is_square_free(self): r""" Returns True if self does not contain squares, and False otherwise. EXAMPLES:: sage: W = Words('123') sage: W('12312').is_square_free() True sage: W('31212').is_square_free() False sage: W().is_square_free() True """ l = self.length() if l < 2: return True suff = self for i in xrange(0,... | 461,708 |
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): TESTS:: sage: P = PolynomialRing(QQ, 0, '') sage: P(5).univariate_polynomial() 5 """ if self.parent().ngens() == 0: if R is None: return self.base_ring()(self) else: return R(self) Returns a univariate polynomial associated to this multivariate polynomial. INPUT: - ``R`` ... | 461,709 |
def factor(self, proof=True): r""" Compute the irreducible factorization of this polynomial. INPUT: - ``proof'' - insist on provably correct results (ignored, always ``True``) ALGORITHM: Use univariate factorization code. If a polynomial is univariate, the appropriate univariate factorization code is called. :: s... | def if self == 0: raise ArithmeticError, "Prime factorization of 0 not defined." if R.ngens() == 0: base_ring = self.base_ring() if base_ring.is_field(): return Factorization([],unit=self.base_ring()(self)) else: F = base_ring(self).factor() return Factorization([(R(f),m) for f,m in F], unit=F.unit()) factor(self, ... | 461,710 |
def is_homogeneous(self, polynomial): r""" Check if ``polynomial`` is homogeneous. | def is_homogeneous(self, polynomial): r""" Check if ``polynomial`` is homogeneous. | 461,711 |
def is_homogeneous(self, polynomial): r""" Check if ``polynomial`` is homogeneous. | def is_homogeneous(self, polynomial): r""" Check if ``polynomial`` is homogeneous. | 461,712 |
def __call__(self, w, order=1, datatype='iter'): r""" Returns the image of ``w`` under self to the given order. INPUT: | def __call__(self, w, order=1, datatype='iter'): r""" Returns the image of ``w`` under self to the given order. INPUT: | 461,713 |
def __call__(self, w, order=1, datatype='iter'): r""" Returns the image of ``w`` under self to the given order. INPUT: | def __call__(self, w, order=1, datatype='iter'): r""" Returns the image of ``w`` under self to the given order. INPUT: | 461,714 |
def __call__(self, w, order=1, datatype='iter'): r""" Returns the image of ``w`` under self to the given order. INPUT: | def __call__(self, w, order=1, datatype='iter'): r""" Returns the image of ``w`` under self to the given order. INPUT: | 461,715 |
def is_prolongable(self, letter): r""" Returns ``True`` if ``self`` is prolongable on ``letter``. A morphism `\varphi` is prolongable on a letter `a` if `a` is a prefix of `\varphi(a)`. INPUT: | def is_prolongable(self, letter): r""" Returns ``True`` if ``self`` is prolongable on ``letter``. A morphism `\varphi` is prolongable on a letter `a` if `a` is a prefix of `\varphi(a)`. INPUT: | 461,716 |
def is_prolongable(self, letter): r""" Returns ``True`` if ``self`` is prolongable on ``letter``. A morphism `\varphi` is prolongable on a letter `a` if `a` is a prefix of `\varphi(a)`. INPUT: | defis_prolongable(self,letter):r"""Returns``True``if``self``isprolongableon``letter``.Amorphism`\varphi`isprolongableonaletter`a`if`a`isaprefixof`\varphi(a)`.INPUT: | 461,717 |
def is_prolongable(self, letter): r""" Returns ``True`` if ``self`` is prolongable on ``letter``. A morphism `\varphi` is prolongable on a letter `a` if `a` is a prefix of `\varphi(a)`. INPUT: | def is_prolongable(self, letter): r""" Returns ``True`` if ``self`` is prolongable on ``letter``. A morphism `\varphi` is prolongable on a letter `a` if `a` is a prefix of `\varphi(a)`. INPUT: | 461,718 |
def letter_iterator(self, letter): r""" Returns an iterator of the letters of the fixed point of ``self`` starting with ``letter``. | def _fixed_point_iterator(self, letter): r""" Returns an iterator of the letters of the fixed point of ``self`` starting with ``letter``. | 461,719 |
def letter_iterator(self, letter): r""" Returns an iterator of the letters of the fixed point of ``self`` starting with ``letter``. | def letter_iterator(self, letter): r""" Returns an iterator of the letters of the fixed point of ``self`` starting with ``letter``. | 461,720 |
def letter_iterator(self, letter): r""" Returns an iterator of the letters of the fixed point of ``self`` starting with ``letter``. | def letter_iterator(self, letter): r""" Returns an iterator of the letters of the fixed point of ``self`` starting with ``letter``. | 461,721 |
def letter_iterator(self, letter): r""" Returns an iterator of the letters of the fixed point of ``self`` starting with ``letter``. | def letter_iterator(self, letter): r""" Returns an iterator of the letters of the fixed point of ``self`` starting with ``letter``. | 461,722 |
def letter_iterator(self, letter): r""" Returns an iterator of the letters of the fixed point of ``self`` starting with ``letter``. | def letter_iterator(self, letter): r""" Returns an iterator of the letters of the fixed point of ``self`` starting with ``letter``. | 461,723 |
def fixed_point(self, letter): r""" Returns the fixed point of ``self`` beginning by the given ``letter``. | def fixed_point(self, letter): r""" Returns the fixed point of ``self`` beginning by the given ``letter``. | 461,724 |
def fixed_point(self, letter): r""" Returns the fixed point of ``self`` beginning by the given ``letter``. | def fixed_point(self, letter): r""" Returns the fixed point of ``self`` beginning by the given ``letter``. | 461,725 |
def eliminate_linear_variables(self, maxlength=3, skip=lambda lm,tail: False): """ Return a new system where "linear variables" are eliminated. | def eliminate_linear_variables(self, maxlength=3, skip=lambda lm,tail: False): """ Return a new system where "linear variables" are eliminated. | 461,726 |
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. | 461,727 |
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. | 461,728 |
def iter_morphisms(self, arg=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | def iter_morphisms(self, arg=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | 461,729 |
def iter_morphisms(self, arg=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | def iter_morphisms(self, arg=None, codomain=None, min_length=1): r""" Iterate over all morphisms with domain ``self`` and the given codmain. | 461,730 |
def spherical_plot3d(f, urange, vrange, **kwds): """ Plots a function in spherical coordinates. This function is equivalent to:: sage: r,u,v=var('r,u,v') sage: f=u*v; urange=(u,0,pi); vrange=(v,0,pi) sage: T = (r*cos(u)*sin(v), r*sin(u)*sin(v), r*cos(v), [u,v]) sage: plot3d(f, urange, vrange, transformation=T) or eq... | def spherical_plot3d(f, urange, vrange, **kwds): """ Plots a function in spherical coordinates. This function is equivalent to:: sage: r,u,v=var('r,u,v') sage: f=u*v; urange=(u,0,pi); vrange=(v,0,pi) sage: T = (r*cos(u)*sin(v), r*sin(u)*sin(v), r*cos(v), [u,v]) sage: plot3d(f, urange, vrange, transformation=T) or eq... | 461,731 |
def vectors_by_length(self, bound): """ Returns a list of short vectors together with their values. This is a naive algorithm which uses the Cholesky decomposition, but does not use the LLL-reduction algorithm. INPUT: bound -- an integer >= 0 OUTPUT: A list L of length (bound + 1) whose entry L[i] is a list of all v... | def vectors_by_length(self, bound): """ Returns a list of short vectors together with their values. This is a naive algorithm which uses the Cholesky decomposition, but does not use the LLL-reduction algorithm. INPUT: bound -- an integer >= 0 OUTPUT: A list L of length (bound + 1) whose entry L[i] is a list of all v... | 461,732 |
def vectors_by_length(self, bound): """ Returns a list of short vectors together with their values. This is a naive algorithm which uses the Cholesky decomposition, but does not use the LLL-reduction algorithm. INPUT: bound -- an integer >= 0 OUTPUT: A list L of length (bound + 1) whose entry L[i] is a list of all v... | def vectors_by_length(self, bound): """ Returns a list of short vectors together with their values. This is a naive algorithm which uses the Cholesky decomposition, but does not use the LLL-reduction algorithm. INPUT: bound -- an integer >= 0 OUTPUT: A list L of length (bound + 1) whose entry L[i] is a list of all v... | 461,733 |
def vectors_by_length(self, bound): """ Returns a list of short vectors together with their values. This is a naive algorithm which uses the Cholesky decomposition, but does not use the LLL-reduction algorithm. INPUT: bound -- an integer >= 0 OUTPUT: A list L of length (bound + 1) whose entry L[i] is a list of all v... | def vectors_by_length(self, bound): """ Returns a list of short vectors together with their values. This is a naive algorithm which uses the Cholesky decomposition, but does not use the LLL-reduction algorithm. INPUT: bound -- an integer >= 0 OUTPUT: A list L of length (bound + 1) whose entry L[i] is a list of all v... | 461,734 |
def vectors_by_length(self, bound): """ Returns a list of short vectors together with their values. This is a naive algorithm which uses the Cholesky decomposition, but does not use the LLL-reduction algorithm. INPUT: bound -- an integer >= 0 OUTPUT: A list L of length (bound + 1) whose entry L[i] is a list of all v... | def vectors_by_length(self, bound): """ Returns a list of short vectors together with their values. This is a naive algorithm which uses the Cholesky decomposition, but does not use the LLL-reduction algorithm. INPUT: bound -- an integer >= 0 OUTPUT: A list L of length (bound + 1) whose entry L[i] is a list of all v... | 461,735 |
def vectors_by_length(self, bound): """ Returns a list of short vectors together with their values. This is a naive algorithm which uses the Cholesky decomposition, but does not use the LLL-reduction algorithm. INPUT: bound -- an integer >= 0 OUTPUT: A list L of length (bound + 1) whose entry L[i] is a list of all v... | def vectors_by_length(self, bound): """ Returns a list of short vectors together with their values. This is a naive algorithm which uses the Cholesky decomposition, but does not use the LLL-reduction algorithm. INPUT: bound -- an integer >= 0 OUTPUT: A list L of length (bound + 1) whose entry L[i] is a list of all v... | 461,736 |
def vectors_by_length(self, bound): """ Returns a list of short vectors together with their values. This is a naive algorithm which uses the Cholesky decomposition, but does not use the LLL-reduction algorithm. INPUT: bound -- an integer >= 0 OUTPUT: A list L of length (bound + 1) whose entry L[i] is a list of all v... | def vectors_by_length(self, bound): """ Returns a list of short vectors together with their values. This is a naive algorithm which uses the Cholesky decomposition, but does not use the LLL-reduction algorithm. INPUT: bound -- an integer >= 0 OUTPUT: A list L of length (bound + 1) whose entry L[i] is a list of all v... | 461,737 |
def run(self, category = None, skip = [], catch = True, raise_on_failure = False, **options): """ Run all the tests from this test suite: | def run(self, category = None, skip = [], catch = True, raise_on_failure = False, **options): """ Run all the tests from this test suite: | 461,738 |
def run(self, category = None, skip = [], catch = True, raise_on_failure = False, **options): """ Run all the tests from this test suite: | def run(self, category = None, skip = [], catch = True, raise_on_failure = False, **options): """ Run all the tests from this test suite: | 461,739 |
def instance_tester(instance, tester = None, **options): """ Returns a gadget attached to ``instance`` providing testing utilities. EXAMPLES:: sage: from sage.misc.sage_unittest import instance_tester sage: tester = instance_tester(ZZ) sage: tester.assert_(1 == 1) sage: tester.assert_(1 == 0) Traceback (most recent ... | def instance_tester(instance, tester = None, **options): """ Returns a gadget attached to ``instance`` providing testing utilities. EXAMPLES:: sage: from sage.misc.sage_unittest import instance_tester sage: tester = instance_tester(ZZ) sage: tester.assert_(1 == 1) sage: tester.assert_(1 == 0) Traceback (most recent ... | 461,740 |
def __init__(self, instance, elements = None, verbose = False, prefix = "", **options): """ A gadget attached to an instance providing it with testing utilities. | def __init__(self, instance, elements = None, verbose = False, prefix = "", **options): """ A gadget attached to an instance providing it with testing utilities. | 461,741 |
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... | 461,742 |
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... | 461,743 |
def _eval_(self, x): """ EXAMPLES:: | def _eval_(self, x): """ EXAMPLES:: | 461,744 |
def _eval_(self, x): """ EXAMPLES:: | def _eval_(self, x): """ EXAMPLES:: | 461,745 |
def _eval_(self, x): """ EXAMPLES:: | def _eval_(self, x): """ EXAMPLES:: | 461,746 |
def rim(self): r""" Returns the rim of ``self`` | def rim(self): r""" Returns the rim of ``self`` | 461,747 |
def rim(self): r""" Returns the rim of ``self`` | def rim(self): r""" Returns the rim of ``self`` | 461,748 |
def outer_rim(self): """ Returns the outer rim of ``self`` | def outer_rim(self): """ Returns the outer rim of ``self`` | 461,749 |
def outer_rim(self): """ Returns the outer rim of ``self`` | def outer_rim(self): """ Returns the outer rim of ``self`` | 461,750 |
def eliminate_linear_variables(self, maxlength=3, skip=lambda lm,tail: False): """ Return a new system where "linear variables" are eliminated. | def eliminate_linear_variables(self, maxlength=3, skip=lambda lm,tail: False): """ Return a new system where "linear variables" are eliminated. | 461,751 |
def associated_primes(self, algorithm='sy'): r""" Return a list of primary ideals (and their associated primes) such that their intersection is `I` = ``self``. An ideal `Q` is called primary if it is a proper ideal of the ring `R` and if whenever `ab \in Q` and `a \not\in Q` then `b^n \in Q` for some `n \in \ZZ`. If ... | def associated_primes(self, algorithm='sy'): r""" Return a list of the associated primes of primary ideals of which the intersection is `I` = ``self``. An ideal `Q` is called primary if it is a proper ideal of the ring `R` and if whenever `ab \in Q` and `a \not\in Q` then `b^n \in Q` for some `n \in \ZZ`. If `Q` is a... | 461,752 |
def associated_primes(self, algorithm='sy'): r""" Return a list of primary ideals (and their associated primes) such that their intersection is `I` = ``self``. An ideal `Q` is called primary if it is a proper ideal of the ring `R` and if whenever `ab \in Q` and `a \not\in Q` then `b^n \in Q` for some `n \in \ZZ`. If ... | defassociated_primes(self,algorithm='sy'):r"""Returnalistofprimaryideals(andtheirassociatedprimes)suchthattheirintersectionis`I`=``self``.Anideal`Q`iscalledprimaryifitisaproperidealofthering`R`andifwhenever`ab\inQ`and`a\not\inQ`then`b^n\inQ`forsome`n\in\ZZ`.If`Q`isaprimaryidealofthering`R`,thentheradicalideal`P`of`Q`,i... | 461,753 |
def associated_primes(self, algorithm='sy'): r""" Return a list of primary ideals (and their associated primes) such that their intersection is `I` = ``self``. An ideal `Q` is called primary if it is a proper ideal of the ring `R` and if whenever `ab \in Q` and `a \not\in Q` then `b^n \in Q` for some `n \in \ZZ`. If ... | def associated_primes(self, algorithm='sy'): r""" Return a list of primary ideals (and their associated primes) such that their intersection is `I` = ``self``. An ideal `Q` is called primary if it is a proper ideal of the ring `R` and if whenever `ab \in Q` and `a \not\in Q` then `b^n \in Q` for some `n \in \ZZ`. If ... | 461,754 |
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. | 461,755 |
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. | 461,756 |
def cospectral_graphs(self, vertices, matrix_function=lambda g: g.adjacency_matrix(), graphs=None): """ Find all sets of graphs on ``vertices`` vertices (with possible restrictions) which are cospectral with respect to a constructed matrix. | def cospectral_graphs(self, vertices, matrix_function=lambda g: g.adjacency_matrix(), graphs=None): r""" Find all sets of graphs on ``vertices`` vertices (with possible restrictions) which are cospectral with respect to a constructed matrix. | 461,757 |
def cospectral_graphs(self, vertices, matrix_function=lambda g: g.adjacency_matrix(), graphs=None): """ Find all sets of graphs on ``vertices`` vertices (with possible restrictions) which are cospectral with respect to a constructed matrix. | def cospectral_graphs(self, vertices, matrix_function=lambda g: g.adjacency_matrix(), graphs=None): """ Find all sets of graphs on ``vertices`` vertices (with possible restrictions) which are cospectral with respect to a constructed matrix. | 461,758 |
def cospectral_graphs(self, vertices, matrix_function=lambda g: g.adjacency_matrix(), graphs=None): """ Find all sets of graphs on ``vertices`` vertices (with possible restrictions) which are cospectral with respect to a constructed matrix. | def cospectral_graphs(self, vertices, matrix_function=lambda g: g.adjacency_matrix(), graphs=None): """ Find all sets of graphs on ``vertices`` vertices (with possible restrictions) which are cospectral with respect to a constructed matrix. | 461,759 |
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... | 461,760 |
def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`. .. warning:: | def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`. .. warning:: | 461,761 |
def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`. .. warning:: | def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`. .. warning:: | 461,762 |
def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`. .. warning:: | def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`. .. warning:: | 461,763 |
def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`. .. warning:: | def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`. .. warning:: | 461,764 |
def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`. .. warning:: | def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`. .. warning:: | 461,765 |
def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`. .. warning:: | defriemann_roch_basis(self,D):r"""ReturnabasisfortheRiemann-Rochspacecorrespondingto`D`...warning:: | 461,766 |
def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`. .. warning:: | def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`. .. warning:: | 461,767 |
def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`. .. warning:: | def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`. .. warning:: | 461,768 |
def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`. .. warning:: | def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`. .. warning:: | 461,769 |
def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`. .. warning:: | def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`. .. warning:: | 461,770 |
def cnf(self, xi=None, yi=None, format=None): """ Return a representation of this S-Box in conjunctive normal form. | def cnf(self, xi=None, yi=None, format=None): """ Return a representation of this S-Box in conjunctive normal form. | 461,771 |
def cnf(self, xi=None, yi=None, format=None): """ Return a representation of this S-Box in conjunctive normal form. | def cnf(self, xi=None, yi=None, format=None): """ Return a representation of this S-Box in conjunctive normal form. | 461,772 |
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun... | def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun... | 461,773 |
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun... | def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun... | 461,774 |
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun... | def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun... | 461,775 |
def str_to_unit(name): """ Create the symbolic unit with given name. A symbolic unit is a class that derives from symbolic expression, and has a specialized docstring. INPUT: - ``name`` -- string OUTPUT: - UnitExpression EXAMPLES:: sage: sage.symbolic.units.str_to_unit('acre') acre sage: type(sage.symbolic.unit... | def str_to_unit(name): """ Create the symbolic unit with given name. A symbolic unit is a class that derives from symbolic expression, and has a specialized docstring. INPUT: - ``name`` -- string OUTPUT: - UnitExpression EXAMPLES:: sage: sage.symbolic.units.str_to_unit('acre') acre sage: type(sage.symbolic.unit... | 461,776 |
def __init__(self, data, name=''): """ EXAMPLES:: | def __init__(self, data, name=''): """ EXAMPLES:: | 461,777 |
def __getattr__(self, name): """ Return the unit with the given name. | def __getattr__(self, name): """ Return the unit with the given name. | 461,778 |
def __repr__(self): """ Return string representation of this collection of units. | def __repr__(self): """ Return string representation of this collection of units. | 461,779 |
def example(self): """ Returns an example of finite permutation group, as per :meth:`Category.example`. | def example(self): """ Returns an example of finite permutation group, as per :meth:`Category.example`. | 461,780 |
def homchain(complex=None, **kwds): r""" Compute the homology of a chain complex using the CHomP program ``homchain``. :param complex: a chain complex :param generators: if True, also return list of generators :type generators: boolean; optional, default False :param verbose: if True, print helpful messages as the com... | def homchain(complex=None, **kwds): r""" Compute the homology of a chain complex using the CHomP program ``homchain``. :param complex: a chain complex :param generators: if True, also return list of generators :type generators: boolean; optional, default False :param verbose: if True, print helpful messages as the com... | 461,781 |
def squarefree_part(x): """ Returns the square free part of `x`, i.e., a divisor `z` such that `x = z y^2`, for a perfect square `y^2`. EXAMPLES:: sage: squarefree_part(100) 1 sage: squarefree_part(12) 3 sage: squarefree_part(10) 10 :: sage: x = QQ['x'].0 sage: S = squarefree_part(-9*x*(x-6)^7*(x-3)^2); S -9*x^2 + ... | def squarefree_part(x): """ Returns the square free part of `x`, i.e., a divisor `z` such that `x = z y^2`, for a perfect square `y^2`. EXAMPLES:: sage: squarefree_part(100) 1 sage: squarefree_part(12) 3 sage: squarefree_part(10) 10 :: sage: x = QQ['x'].0 sage: S = squarefree_part(-9*x*(x-6)^7*(x-3)^2); S -9*x^2 + ... | 461,782 |
def inject_coefficients(self, scope=None, verbose=True): r""" Inject generators of the base field of ``self`` into ``scope``. | def inject_coefficients(self, scope=None, verbose=True): r""" Inject generators of the base field of ``self`` into ``scope``. | 461,783 |
def inject_coefficients(self, scope=None, verbose=True): r""" Inject generators of the base field of ``self`` into ``scope``. | def inject_coefficients(self, scope=None, verbose=True): r""" Inject generators of the base field of ``self`` into ``scope``. | 461,784 |
def inject_coefficients(self, scope=None, verbose=True): r""" Inject generators of the base field of ``self`` into ``scope``. | def inject_coefficients(self, scope=None, verbose=True): r""" Inject generators of the base field of ``self`` into ``scope``. | 461,785 |
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. | 461,786 |
def is_integral_domain(self, proof = True): r""" If this function returns ``True`` then self is definitely an integral domain. If it returns ``False``, then either self is definitely not an integral domain or this function was unable to determine whether or not self is an integral domain. Use ``self.defining_ideal().i... | def is_integral_domain(self, proof=True): r""" With ``proof`` equal to ``True`` (the default), this function may raise a ``NotImplementedError``. When ``proof`` is ``False``, if ``True`` is returned, then self is definitely an integral domain. If the function returns ``False``, then either self is not an integral do... | 461,787 |
def is_integral_domain(self, proof = True): r""" If this function returns ``True`` then self is definitely an integral domain. If it returns ``False``, then either self is definitely not an integral domain or this function was unable to determine whether or not self is an integral domain. Use ``self.defining_ideal().i... | def is_integral_domain(self, proof = True): r""" If this function returns ``True`` then self is definitely an integral domain. If it returns ``False``, then either self is definitely not an integral domain or this function was unable to determine whether or not self is an integral domain. Use ``self.defining_ideal().i... | 461,788 |
def is_integral_domain(self, proof = True): r""" If this function returns ``True`` then self is definitely an integral domain. If it returns ``False``, then either self is definitely not an integral domain or this function was unable to determine whether or not self is an integral domain. Use ``self.defining_ideal().i... | def is_integral_domain(self, proof = True): r""" If this function returns ``True`` then self is definitely an integral domain. If it returns ``False``, then either self is definitely not an integral domain or this function was unable to determine whether or not self is an integral domain. Use ``self.defining_ideal().i... | 461,789 |
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`. | 461,790 |
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`. | 461,791 |
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`. | 461,792 |
def __init__(self, *args, **kwargs): """ Construct a substitution box (S-box) for a given lookup table `S`. | def if not ZZ(len(S)).is_power_of(2): raise TypeError("Lookup table length is not a power of 2.") __init__(self, if not ZZ(len(S)).is_power_of(2): raise TypeError("Lookup table length is not a power of 2.") *args, if not ZZ(len(S)).is_power_of(2): raise TypeError("Lookup table length is not a power of 2.") if not ZZ(l... | 461,793 |
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`. | 461,794 |
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun... | def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun... | 461,795 |
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun... | def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun... | 461,796 |
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun... | def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun... | 461,797 |
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun... | def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun... | 461,798 |
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun... | def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun... | 461,799 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.