bugged stringlengths 4 228k | fixed stringlengths 0 96.3M | __index_level_0__ int64 0 481k |
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def random_prime(n, proof=None, lbound=2): """ Returns a random prime p between `lbound` and n (i.e. `lbound <= p <= n`). The returned prime is chosen uniformly at random from the set of prime numbers less than or equal to n. INPUT: - ``n`` - an integer >= 2. - ``proof`` - bool or None (default: None) If False, th... | def random_prime(n, proof=None, lbound=2): """ Returns a random prime p between `lbound` and n (i.e. `lbound <= p <= n`). The returned prime is chosen uniformly at random from the set of prime numbers less than or equal to n. INPUT: - ``n`` - an integer >= 2. - ``proof`` - bool or None (default: None) If False, th... | 472,800 |
def random_prime(n, proof=None, lbound=2): """ Returns a random prime p between `lbound` and n (i.e. `lbound <= p <= n`). The returned prime is chosen uniformly at random from the set of prime numbers less than or equal to n. INPUT: - ``n`` - an integer >= 2. - ``proof`` - bool or None (default: None) If False, th... | def random_prime(n, proof=None, lbound=2): """ Returns a random prime p between `lbound` and n (i.e. `lbound <= p <= n`). The returned prime is chosen uniformly at random from the set of prime numbers less than or equal to n. INPUT: - ``n`` - an integer >= 2. - ``proof`` - bool or None (default: None) If False, th... | 472,801 |
def random_prime(n, proof=None, lbound=2): """ Returns a random prime p between `lbound` and n (i.e. `lbound <= p <= n`). The returned prime is chosen uniformly at random from the set of prime numbers less than or equal to n. INPUT: - ``n`` - an integer >= 2. - ``proof`` - bool or None (default: None) If False, th... | def random_prime(n, proof=None, lbound=2): """ Returns a random prime p between `lbound` and n (i.e. `lbound <= p <= n`). The returned prime is chosen uniformly at random from the set of prime numbers less than or equal to n. INPUT: - ``n`` - an integer >= 2. - ``proof`` - bool or None (default: None) If False, th... | 472,802 |
def __cmp__(self, right): r""" Compare ``self`` and ``right``. | def __cmp__(self, right): r""" Compare ``self`` and ``right``. | 472,803 |
def taylor(f, v, a, n): """ Expands self in a truncated Taylor or Laurent series in the variable `v` around the point `a`, containing terms through `(x - a)^n`. INPUT: - ``v`` - variable - ``a`` - number - ``n`` - integer EXAMPLES:: sage: var('x,k,n') (x, k, n) sage: taylor (sqrt (1 - k^2*sin(x)^2), x, 0, 6) -... | def taylor(f, *args): """ Expands self in a truncated Taylor or Laurent series in the variable `v` around the point `a`, containing terms through `(x - a)^n`. INPUT: - ``v`` - variable - ``a`` - number - ``n`` - integer EXAMPLES:: sage: var('x,k,n') (x, k, n) sage: taylor (sqrt (1 - k^2*sin(x)^2), x, 0, 6) -1/... | 472,804 |
def taylor(f, v, a, n): """ Expands self in a truncated Taylor or Laurent series in the variable `v` around the point `a`, containing terms through `(x - a)^n`. INPUT: - ``v`` - variable - ``a`` - number - ``n`` - integer EXAMPLES:: sage: var('x,k,n') (x, k, n) sage: taylor (sqrt (1 - k^2*sin(x)^2), x, 0, 6) -... | def taylor(f, v, a, n): """ Expands self in a truncated Taylor or Laurent series in the variable `v` around the point `a`, containing terms through `(x - a)^n`. Functions in more variables are also supported. INPUT: - ``v`` - variable - ``a`` - number - ``n`` - integer EXAMPLES:: sage: var('x,k,n') (x, k, n) s... | 472,805 |
def taylor(f, v, a, n): """ Expands self in a truncated Taylor or Laurent series in the variable `v` around the point `a`, containing terms through `(x - a)^n`. INPUT: - ``v`` - variable - ``a`` - number - ``n`` - integer EXAMPLES:: sage: var('x,k,n') (x, k, n) sage: taylor (sqrt (1 - k^2*sin(x)^2), x, 0, 6) -... | def taylor(f, v, a, n): """ Expands self in a truncated Taylor or Laurent series in the variable `v` around the point `a`, containing terms through `(x - a)^n`. INPUT: - ``*args`` - the following notation is supported - ``x, a, n`` - variable, point, degree - ``(x, a), (y, b), ..., n`` - variables with points, deg... | 472,806 |
def taylor(f, v, a, n): """ Expands self in a truncated Taylor or Laurent series in the variable `v` around the point `a`, containing terms through `(x - a)^n`. INPUT: - ``v`` - variable - ``a`` - number - ``n`` - integer EXAMPLES:: sage: var('x,k,n') (x, k, n) sage: taylor (sqrt (1 - k^2*sin(x)^2), x, 0, 6) -... | def taylor(f, v, a, n): """ Expands self in a truncated Taylor or Laurent series in the variable `v` around the point `a`, containing terms through `(x - a)^n`. INPUT: - ``v`` - variable - ``a`` - number - ``n`` - integer EXAMPLES:: sage: var('x,k,n') (x, k, n) sage: taylor (sqrt (1 - k^2*sin(x)^2), x, 0, 6) -... | 472,807 |
def derivative(self, ex, operator): """ EXAMPLES:: | def derivative(self, ex, operator): """ EXAMPLES:: | 472,808 |
def derivative(self, ex, operator): """ EXAMPLES:: | def derivative(self, ex, operator): """ EXAMPLES:: | 472,809 |
def derivative(self, ex, operator): """ EXAMPLES:: | def derivative(self, ex, operator): """ EXAMPLES:: | 472,810 |
def derivative(self, ex, operator): """ EXAMPLES:: | def derivative(self, ex, operator): """ EXAMPLES:: | 472,811 |
sage: def naive_height(P): | sage: def naive_height(P): | 472,812 |
sage: def is_4regular(G): | sage: def is_4regular(G): | 472,813 |
def max_cut(self, value_only=True, use_edge_labels=True, vertices=False, solver=None, verbose=0): r""" Returns a maximum edge cut of the graph. For more information, see the `Wikipedia article on cuts <http://en.wikipedia.org/wiki/Cut_%28graph_theory%29>`_. | def max_cut(self, value_only=True, use_edge_labels=True, vertices=False, solver=None, verbose=0): r""" Returns a maximum edge cut of the graph. For more information, see the `Wikipedia article on cuts <http://en.wikipedia.org/wiki/Cut_%28graph_theory%29>`_. | 472,814 |
def max_cut(self, value_only=True, use_edge_labels=True, vertices=False, solver=None, verbose=0): r""" Returns a maximum edge cut of the graph. For more information, see the `Wikipedia article on cuts <http://en.wikipedia.org/wiki/Cut_%28graph_theory%29>`_. | def max_cut(self, value_only=True, use_edge_labels=True, vertices=False, solver=None, verbose=0): r""" Returns a maximum edge cut of the graph. For more information, see the `Wikipedia article on cuts <http://en.wikipedia.org/wiki/Cut_%28graph_theory%29>`_. | 472,815 |
def max_cut(self, value_only=True, use_edge_labels=True, vertices=False, solver=None, verbose=0): r""" Returns a maximum edge cut of the graph. For more information, see the `Wikipedia article on cuts <http://en.wikipedia.org/wiki/Cut_%28graph_theory%29>`_. | def max_cut(self, value_only=True, use_edge_labels=True, vertices=False, solver=None, verbose=0): r""" Returns a maximum edge cut of the graph. For more information, see the `Wikipedia article on cuts <http://en.wikipedia.org/wiki/Cut_%28graph_theory%29>`_. | 472,816 |
def flow(self, x, y, value_only=True, integer=False, use_edge_labels=True, vertex_bound=False, solver=None, verbose=0): r""" Returns a maximum flow in the graph from ``x`` to ``y`` represented by an optimal valuation of the edges. For more information, see the `Wikipedia article on maximum flow <http://en.wikipedia.org... | def flow(self, x, y, value_only=True, integer=False, use_edge_labels=True, vertex_bound=False, solver=None, verbose=0): r""" Returns a maximum flow in the graph from ``x`` to ``y`` represented by an optimal valuation of the edges. For more information, see the `Wikipedia article on maximum flow <http://en.wikipedia.org... | 472,817 |
def flow(self, x, y, value_only=True, integer=False, use_edge_labels=True, vertex_bound=False, solver=None, verbose=0): r""" Returns a maximum flow in the graph from ``x`` to ``y`` represented by an optimal valuation of the edges. For more information, see the `Wikipedia article on maximum flow <http://en.wikipedia.org... | def flow(self, x, y, value_only=True, integer=False, use_edge_labels=True, vertex_bound=False, solver=None, verbose=0): r""" Returns a maximum flow in the graph from ``x`` to ``y`` represented by an optimal valuation of the edges. For more information, see the `Wikipedia article on maximum flow <http://en.wikipedia.org... | 472,818 |
def dominating_set(self, independent=False, value_only=False, solver=None, verbose=0): r""" Returns a minimum dominating set of the graph represented by the list of its vertices. For more information, see the `Wikipedia article on dominating sets <http://en.wikipedia.org/wiki/Dominating_set>`_. | def dominating_set(self, independent=False, value_only=False, solver=None, verbose=0): r""" Returns a minimum dominating set of the graph represented by the list of its vertices. For more information, see the `Wikipedia article on dominating sets <http://en.wikipedia.org/wiki/Dominating_set>`_. | 472,819 |
def dominating_set(self, independent=False, value_only=False, solver=None, verbose=0): r""" Returns a minimum dominating set of the graph represented by the list of its vertices. For more information, see the `Wikipedia article on dominating sets <http://en.wikipedia.org/wiki/Dominating_set>`_. | def dominating_set(self, independent=False, value_only=False, solver=None, verbose=0): r""" Returns a minimum dominating set of the graph represented by the list of its vertices. For more information, see the `Wikipedia article on dominating sets <http://en.wikipedia.org/wiki/Dominating_set>`_. | 472,820 |
def dominating_set(self, independent=False, value_only=False, solver=None, verbose=0): r""" Returns a minimum dominating set of the graph represented by the list of its vertices. For more information, see the `Wikipedia article on dominating sets <http://en.wikipedia.org/wiki/Dominating_set>`_. | def dominating_set(self, independent=False, value_only=False, solver=None, verbose=0): r""" Returns a minimum dominating set of the graph represented by the list of its vertices. For more information, see the `Wikipedia article on dominating sets <http://en.wikipedia.org/wiki/Dominating_set>`_. | 472,821 |
def edge_connectivity(self, value_only=True, use_edge_labels=False, vertices=False, solver=None, verbose=0): r""" Returns the edge connectivity of the graph. For more information, see the `Wikipedia article on connectivity <http://en.wikipedia.org/wiki/Connectivity_(graph_theory)>`_. | def edge_connectivity(self, value_only=True, use_edge_labels=False, vertices=False, solver=None, verbose=0): r""" Returns the edge connectivity of the graph. For more information, see the `Wikipedia article on connectivity <http://en.wikipedia.org/wiki/Connectivity_(graph_theory)>`_. | 472,822 |
def edge_connectivity(self, value_only=True, use_edge_labels=False, vertices=False, solver=None, verbose=0): r""" Returns the edge connectivity of the graph. For more information, see the `Wikipedia article on connectivity <http://en.wikipedia.org/wiki/Connectivity_(graph_theory)>`_. | def edge_connectivity(self, value_only=True, use_edge_labels=False, vertices=False, solver=None, verbose=0): r""" Returns the edge connectivity of the graph. For more information, see the `Wikipedia article on connectivity <http://en.wikipedia.org/wiki/Connectivity_(graph_theory)>`_. | 472,823 |
def edge_connectivity(self, value_only=True, use_edge_labels=False, vertices=False, solver=None, verbose=0): r""" Returns the edge connectivity of the graph. For more information, see the `Wikipedia article on connectivity <http://en.wikipedia.org/wiki/Connectivity_(graph_theory)>`_. | def edge_connectivity(self, value_only=True, use_edge_labels=False, vertices=False, solver=None, verbose=0): r""" Returns the edge connectivity of the graph. For more information, see the `Wikipedia article on connectivity <http://en.wikipedia.org/wiki/Connectivity_(graph_theory)>`_. | 472,824 |
def edge_connectivity(self, value_only=True, use_edge_labels=False, vertices=False, solver=None, verbose=0): r""" Returns the edge connectivity of the graph. For more information, see the `Wikipedia article on connectivity <http://en.wikipedia.org/wiki/Connectivity_(graph_theory)>`_. | def edge_connectivity(self, value_only=True, use_edge_labels=False, vertices=False, solver=None, verbose=0): r""" Returns the edge connectivity of the graph. For more information, see the `Wikipedia article on connectivity <http://en.wikipedia.org/wiki/Connectivity_(graph_theory)>`_. | 472,825 |
def edge_connectivity(self, value_only=True, use_edge_labels=False, vertices=False, solver=None, verbose=0): r""" Returns the edge connectivity of the graph. For more information, see the `Wikipedia article on connectivity <http://en.wikipedia.org/wiki/Connectivity_(graph_theory)>`_. | def edge_connectivity(self, value_only=True, use_edge_labels=False, vertices=False, solver=None, verbose=0): r""" Returns the edge connectivity of the graph. For more information, see the `Wikipedia article on connectivity <http://en.wikipedia.org/wiki/Connectivity_(graph_theory)>`_. | 472,826 |
def edge_connectivity(self, value_only=True, use_edge_labels=False, vertices=False, solver=None, verbose=0): r""" Returns the edge connectivity of the graph. For more information, see the `Wikipedia article on connectivity <http://en.wikipedia.org/wiki/Connectivity_(graph_theory)>`_. | def edge_connectivity(self, value_only=True, use_edge_labels=False, vertices=False, solver=None, verbose=0): r""" Returns the edge connectivity of the graph. For more information, see the `Wikipedia article on connectivity <http://en.wikipedia.org/wiki/Connectivity_(graph_theory)>`_. | 472,827 |
def vertex_connectivity(self, value_only=True, sets=False, solver=None, verbose=0): r""" Returns the vertex connectivity of the graph. For more information, see the `Wikipedia article on connectivity <http://en.wikipedia.org/wiki/Connectivity_(graph_theory)>`_. | def vertex_connectivity(self, value_only=True, sets=False, solver=None, verbose=0): r""" Returns the vertex connectivity of the graph. For more information, see the `Wikipedia article on connectivity <http://en.wikipedia.org/wiki/Connectivity_(graph_theory)>`_. | 472,828 |
def vertex_connectivity(self, value_only=True, sets=False, solver=None, verbose=0): r""" Returns the vertex connectivity of the graph. For more information, see the `Wikipedia article on connectivity <http://en.wikipedia.org/wiki/Connectivity_(graph_theory)>`_. | def vertex_connectivity(self, value_only=True, sets=False, solver=None, verbose=0): r""" Returns the vertex connectivity of the graph. For more information, see the `Wikipedia article on connectivity <http://en.wikipedia.org/wiki/Connectivity_(graph_theory)>`_. | 472,829 |
def vertex_connectivity(self, value_only=True, sets=False, solver=None, verbose=0): r""" Returns the vertex connectivity of the graph. For more information, see the `Wikipedia article on connectivity <http://en.wikipedia.org/wiki/Connectivity_(graph_theory)>`_. | def vertex_connectivity(self, value_only=True, sets=False, solver=None, verbose=0): r""" Returns the vertex connectivity of the graph. For more information, see the `Wikipedia article on connectivity <http://en.wikipedia.org/wiki/Connectivity_(graph_theory)>`_. | 472,830 |
def layout_graphviz(self, dim = 2, prog = 'dot', **options): """ Calls ``graphviz`` to compute a layout of the vertices of this graph. | def layout_graphviz(self, dim = 2, prog = 'dot', **options): """ Calls ``graphviz`` to compute a layout of the vertices of this graph. | 472,831 |
def layout_graphviz(self, dim = 2, prog = 'dot', **options): """ Calls ``graphviz`` to compute a layout of the vertices of this graph. | def layout_graphviz(self, dim = 2, prog = 'dot', **options): """ Calls ``graphviz`` to compute a layout of the vertices of this graph. | 472,832 |
def layout_graphviz(self, dim = 2, prog = 'dot', **options): """ Calls ``graphviz`` to compute a layout of the vertices of this graph. | def layout_graphviz(self, dim = 2, prog = 'dot', **options): """ Calls ``graphviz`` to compute a layout of the vertices of this graph. | 472,833 |
def layout_graphviz(self, dim = 2, prog = 'dot', **options): """ Calls ``graphviz`` to compute a layout of the vertices of this graph. | def layout_graphviz(self, dim = 2, prog = 'dot', **options): """ Calls ``graphviz`` to compute a layout of the vertices of this graph. | 472,834 |
def plot(self, *args, **kwds): """ The R plot function. Type r.help('plot') for much more extensive documentation about this function. See also below for a brief introduction to more plotting with R. | def plot(self, *args, **kwds): """ The R plot function. Type r.help('plot') for much more extensive documentation about this function. See also below for a brief introduction to more plotting with R. | 472,835 |
def plot(self, *args, **kwds): """ The R plot function. Type r.help('plot') for much more extensive documentation about this function. See also below for a brief introduction to more plotting with R. | def plot(self, *args, **kwds): """ The R plot function. Type r.help('plot') for much more extensive documentation about this function. See also below for a brief introduction to more plotting with R. | 472,836 |
def is_submodule(self, other): """ Return True if self is a submodule of other. | def is_submodule(self, other): """ Return True if self is a submodule of other. | 472,837 |
def FuzzyBallGraph(self, partition, q): """ Construct a Fuzzy Ball graph with the integer partition ``partition`` and ``q`` extra vertices. | def FuzzyBallGraph(self, partition, q): r""" Construct a Fuzzy Ball graph with the integer partition ``partition`` and ``q`` extra vertices. | 472,838 |
def FuzzyBallGraph(self, partition, q): """ Construct a Fuzzy Ball graph with the integer partition ``partition`` and ``q`` extra vertices. | def FuzzyBallGraph(self, partition, q): """ Construct a Fuzzy Ball graph with the integer partition ``partition`` and ``q`` extra vertices. | 472,839 |
def FuzzyBallGraph(self, partition, q): """ Construct a Fuzzy Ball graph with the integer partition ``partition`` and ``q`` extra vertices. | def FuzzyBallGraph(self, partition, q): """ Construct a Fuzzy Ball graph with the integer partition ``partition`` and ``q`` extra vertices. | 472,840 |
def eigenvalues(self,extend=True): """ Returns a list with the eigenvalues of the endomorphism of vector spaces. | def eigenvalues(self,extend=True): r""" Returns a list with the eigenvalues of the endomorphism of vector spaces. | 472,841 |
def eigenvalues(self,extend=True): """ Returns a list with the eigenvalues of the endomorphism of vector spaces. | def eigenvalues(self,extend=True): """ Returns a list with the eigenvalues of the endomorphism of vector spaces. | 472,842 |
def eigenvalues(self,extend=True): """ Returns a list with the eigenvalues of the endomorphism of vector spaces. | def eigenvalues(self,extend=True): """ Returns a list with the eigenvalues of the endomorphism of vector spaces. | 472,843 |
def eigenvalues(self,extend=True): """ Returns a list with the eigenvalues of the endomorphism of vector spaces. | def eigenvalues(self,extend=True): """ Returns a list with the eigenvalues of the endomorphism of vector spaces. | 472,844 |
def eigenvalues(self,extend=True): """ Returns a list with the eigenvalues of the endomorphism of vector spaces. | defeigenvalues(self,extend=True):"""Returnsalistwiththeeigenvaluesoftheendomorphismofvectorspaces. | 472,845 |
def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. | def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. | 472,846 |
def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. | def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. | 472,847 |
def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. | def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. | 472,848 |
def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. | def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. | 472,849 |
def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. | def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. | 472,850 |
def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. | def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. | 472,851 |
def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. | def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. | 472,852 |
def minpoly(self,var='x'): """ Computes the minimal polynomial. | def minpoly(self,var='x'): """ Computes the minimal polynomial. | 472,853 |
def star_generator_indices(self): r""" Return indices of generating cones of the "ambient fan" containing ``self``. | def star_generator_indices(self): r""" Return indices of generating cones of the "ambient fan" containing ``self``. | 472,854 |
def WeylCharacterRing(ct, base_ring=ZZ, prefix=None, cache=False, style="lattice"): r""" A class for rings of Weyl characters. The Weyl character is a character of a semisimple (or reductive) Lie group or algebra. They form a ring, in which the addition and multiplication correspond to direct sum and tensor product of ... | def WeylCharacterRing(ct, base_ring=ZZ, prefix=None, cache=False, style="lattice"): r""" A class for rings of Weyl characters. The Weyl character is a character of a semisimple (or reductive) Lie group or algebra. They form a ring, in which the addition and multiplication correspond to direct sum and tensor product of ... | 472,855 |
def branch_weyl_character(chi, R, S, rule="default"): r""" A Branching rule describes the restriction of representations from a Lie group or algebra G to a smaller one. See for example, R. C. King, Branching rules for classical Lie groups using tensor and spinor methods. J. Phys. A 8 (1975), 429-449, Howe, Tan and Will... | def branch_weyl_character(chi, R, S, rule="default"): r""" A Branching rule describes the restriction of representations from a Lie group or algebra G to a smaller one. See for example, R. C. King, Branching rules for classical Lie groups using tensor and spinor methods. J. Phys. A 8 (1975), 429-449, Howe, Tan and Will... | 472,856 |
def branch_weyl_character(chi, R, S, rule="default"): r""" A Branching rule describes the restriction of representations from a Lie group or algebra G to a smaller one. See for example, R. C. King, Branching rules for classical Lie groups using tensor and spinor methods. J. Phys. A 8 (1975), 429-449, Howe, Tan and Will... | def branch_weyl_character(chi, R, S, rule="default"): r""" A Branching rule describes the restriction of representations from a Lie group or algebra G to a smaller one. See for example, R. C. King, Branching rules for classical Lie groups using tensor and spinor methods. J. Phys. A 8 (1975), 429-449, Howe, Tan and Will... | 472,857 |
def branch_weyl_character(chi, R, S, rule="default"): r""" A Branching rule describes the restriction of representations from a Lie group or algebra G to a smaller one. See for example, R. C. King, Branching rules for classical Lie groups using tensor and spinor methods. J. Phys. A 8 (1975), 429-449, Howe, Tan and Will... | def branch_weyl_character(chi, R, S, rule="default"): r""" A Branching rule describes the restriction of representations from a Lie group or algebra G to a smaller one. See for example, R. C. King, Branching rules for classical Lie groups using tensor and spinor methods. J. Phys. A 8 (1975), 429-449, Howe, Tan and Will... | 472,858 |
def rule(x) : x[len(x)-1] = -x[len(x)-1]; return x | def rule(x) : x[len(x)-1] = -x[len(x)-1]; return x | 472,859 |
def __call__(self, *args): """ Coerces the element into the ring. | def __call__(self, *args): """ Coerces the element into the ring. | 472,860 |
def _magma_init_(self, magma): r""" EXAMPLES: We first coerce a square matrix. | def _magma_init_(self, magma): r""" EXAMPLES: We first coerce a square matrix. | 472,861 |
def _magma_init_(self, magma): r""" EXAMPLES: We first coerce a square matrix. | def _magma_init_(self, magma): r""" EXAMPLES: We first coerce a square matrix. | 472,862 |
def _magma_init_(self, magma): r""" EXAMPLES: We first coerce a square matrix. | def _magma_init_(self, magma): r""" EXAMPLES: We first coerce a square matrix. | 472,863 |
def bistochastic_as_sum_of_permutations(M, check = True): r""" Returns the positive sum of permutations corresponding to the bistochastic matrix. A stochastic matrix is a matrix such that the sum of the elements of any row is equal to 1. A bistochastic matrix is a stochastic matrix whose transpose matrix is also stoch... | def bistochastic_as_sum_of_permutations(M, check = True): r""" Returns the positive sum of permutations corresponding to the bistochastic matrix. A stochastic matrix is a matrix with nonnegative real entries such that the sum of the elements of any row is equal to 1. A bistochastic matrix is a stochastic matrix whose ... | 472,864 |
def bistochastic_as_sum_of_permutations(M, check = True): r""" Returns the positive sum of permutations corresponding to the bistochastic matrix. A stochastic matrix is a matrix such that the sum of the elements of any row is equal to 1. A bistochastic matrix is a stochastic matrix whose transpose matrix is also stoch... | def bistochastic_as_sum_of_permutations(M, check = True): r""" Returns the positive sum of permutations corresponding to the bistochastic matrix. A stochastic matrix is a matrix such that the sum of the elements of any row is equal to 1. A bistochastic matrix is a stochastic matrix whose transpose matrix is also stoch... | 472,865 |
def bistochastic_as_sum_of_permutations(M, check = True): r""" Returns the positive sum of permutations corresponding to the bistochastic matrix. A stochastic matrix is a matrix such that the sum of the elements of any row is equal to 1. A bistochastic matrix is a stochastic matrix whose transpose matrix is also stoch... | def bistochastic_as_sum_of_permutations(M, check = True): r""" Returns the positive sum of permutations corresponding to the bistochastic matrix. A stochastic matrix is a matrix such that the sum of the elements of any row is equal to 1. A bistochastic matrix is a stochastic matrix whose transpose matrix is also stoch... | 472,866 |
def bistochastic_as_sum_of_permutations(M, check = True): r""" Returns the positive sum of permutations corresponding to the bistochastic matrix. A stochastic matrix is a matrix such that the sum of the elements of any row is equal to 1. A bistochastic matrix is a stochastic matrix whose transpose matrix is also stoch... | def bistochastic_as_sum_of_permutations(M, check = True): r""" Returns the positive sum of permutations corresponding to the bistochastic matrix. A stochastic matrix is a matrix such that the sum of the elements of any row is equal to 1. A bistochastic matrix is a stochastic matrix whose transpose matrix is also stoch... | 472,867 |
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 | 472,868 |
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 | 472,869 |
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 | 472,870 |
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 | 472,871 |
def CPS_height_bound(self): r""" Return the Cremona-Prickett-Siksek height bound. This is a floating point number B such that if P is a rational point on the curve, then `|h(P) - \hat{h}(P)| \leq B`, where `h(P)` is the naive logarithmic height of `P` and `\hat{h}(P)` is the canonical height. | def CPS_height_bound(self): r""" Return the Cremona-Prickett-Siksek height bound. This is a floating point number B such that if P is a rational point on the curve, then `h(P) \le \hat{h}(P) + B`, where `h(P)` is the naive logarithmic height of `P` and `\hat{h}(P)` is the canonical height. | 472,872 |
def LyndonWords(e=None, k=None): """ Returns the combinatorial class of Lyndon words. A Lyndon word `w` is a word that is lexicographically less than all of its rotations. Equivalently, whenever `w` is split into two non-empty substrings, `w` is lexicographically less than the right substring. INPUT: - no input at ... | def LyndonWords(e=None, k=None): """ Returns the combinatorial class of Lyndon words. A Lyndon word `w` is a word that is lexicographically less than all of its rotations. Equivalently, whenever `w` is split into two non-empty substrings, `w` is lexicographically less than the right substring. INPUT: - no input at ... | 472,873 |
def LyndonWords(e=None, k=None): """ Returns the combinatorial class of Lyndon words. A Lyndon word `w` is a word that is lexicographically less than all of its rotations. Equivalently, whenever `w` is split into two non-empty substrings, `w` is lexicographically less than the right substring. INPUT: - no input at ... | def LyndonWords(e=None, k=None): """ Returns the combinatorial class of Lyndon words. A Lyndon word `w` is a word that is lexicographically less than all of its rotations. Equivalently, whenever `w` is split into two non-empty substrings, `w` is lexicographically less than the right substring. INPUT: - no input at ... | 472,874 |
def __init__(self, data, check=True): r""" Construction of a Lyndon word. | def __init__(self, data, check=True): r""" Construction of a Lyndon word. | 472,875 |
def __init__(self, data, check=True): r""" Construction of a Lyndon word. | def __init__(self, data, check=True): r""" Construction of a Lyndon word. | 472,876 |
def _pcubicroots(b, c, d): r""" Local function returning the number of roots of `x^3 + b*x^2 + c*x + d` modulo `P`, counting multiplicities """ return sum([rr[1] for rr in PolynomialRing(F, 'x')([d, c, b, 1]).roots()],0) | def _pcubicroots(b, c, d): r""" Local function returning the number of roots of `x^3 + b*x^2 + c*x + d` modulo `P`, counting multiplicities """ return sum([rr[1] for rr in PolynomialRing(F, 'x')([d, c, b, 1]).roots()],0) | 472,877 |
def univariate_polynomial(self, R=None): """ Returns a univariate polynomial associated to this multivariate polynomial. | 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. | 472,878 |
def factor(self, proof=True): r""" Compute the irreducible factorization of this polynomial. | 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, ... | 472,879 |
def _eval_(self, x): """ | def _eval_(self, x): """ | 472,880 |
def _eval_(self, x): """ | def _eval_(self, x): """ | 472,881 |
def _eval_(self, x): """ | def _eval_(self, x): """ | 472,882 |
def transform(self, **kwds): """ EXAMPLE:: | def transform(self, **kwds): """ EXAMPLE:: | 472,883 |
def transform(self, radius=None, azimuth=None, inclination=None): """ A spherical coordinates transform. | def transform(self, radius=None, azimuth=None, inclination=None): """ A spherical coordinates transform. | 472,884 |
def univariate_polynomial(self, R=None): """ Returns a univariate polynomial associated to this multivariate polynomial. | def univariate_polynomial(self, R=None): """ Returns a univariate polynomial associated to this multivariate polynomial. | 472,885 |
def prime_to_S_part(self,S): r""" This function returns the part of the fractional ideal self which is coprime to the prime ideals in the list S | def prime_to_S_part(self,S): r""" This function returns the part of the fractional ideal self which is coprime to the prime ideals in the list S | 472,886 |
def prime_to_S_part(self,S): r""" This function returns the part of the fractional ideal self which is coprime to the prime ideals in the list S | def prime_to_S_part(self,S): r""" This function returns the part of the fractional ideal self which is coprime to the prime ideals in the list S | 472,887 |
def prime_to_S_part(self,S): r""" This function returns the part of the fractional ideal self which is coprime to the prime ideals in the list S | def prime_to_S_part(self,S): r""" This function returns the part of the fractional ideal self which is coprime to the prime ideals in the list S | 472,888 |
def is_S_unit(self,S): r''' Returns True if the ideal is an unit with respect to the | def is_S_unit(self,S): r''' Returns True if the ideal is an unit with respect to the | 472,889 |
def is_S_unit(self,S): r''' Returns True if the ideal is an unit with respect to the | def is_S_unit(self,S): r""" Returns True if the ideal is an unit with respect to the | 472,890 |
def is_S_integral(self,S): r''' Returns True if the ideal is an unit with respect to the | def is_S_integral(self,S): r''' Returns True if the ideal is an unit with respect to the | 472,891 |
def is_S_integral(self,S): r''' Returns True if the ideal is an unit with respect to the | def is_S_integral(self,S): r""" Returns True if the ideal is an unit with respect to the | 472,892 |
def __init__(self, s): """ TESTS:: | def __init__(self, s): """ TESTS:: | 472,893 |
def unrank(self, r): """ Returns the subset of s that has rank k. | def unrank(self, r): """ Returns the subset of s that has rank k. | 472,894 |
def __init__(self, s, k): """ TESTS:: | def __init__(self, s, k): """ TESTS:: | 472,895 |
def unrank(self, r): """ Returns the subset of s that has rank k. | def unrank(self, r): """ Returns the subset of s that has rank k. | 472,896 |
def unrank(self, r): """ Returns the subset of s that has rank k. | def unrank(self, r): """ Returns the subset of s that has rank k. | 472,897 |
def __iter__(self): """ Iterates through the subsets of the multiset ``self._s``. Note that each subset is represented by a list of its elements rather than a set since we can have multiplicities (no multiset data structure yet in sage). | def __iter__(self): """ Iterates through the subsets of the multiset ``self._s``. Note that each subset is represented by a list of its elements rather than a set since we can have multiplicities (no multiset data structure yet in sage). | 472,898 |
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... | 472,899 |
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