bugged stringlengths 4 228k | fixed stringlengths 0 96.3M | __index_level_0__ int64 0 481k |
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def rank_bounds(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns the lower and upper bounds using simon_two_descent. The results of simon_two_descent are cached. | def rank_bounds(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns the lower and upper bounds using simon_two_descent. The results of simon_two_descent are cached. | 460,600 |
def rank_bounds(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns the lower and upper bounds using simon_two_descent. The results of simon_two_descent are cached. | def rank_bounds(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns the lower and upper bounds using simon_two_descent. The results of simon_two_descent are cached. | 460,601 |
def rank(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Return the rank of this elliptic curve, if it can be determined. | def rank(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Return the rank of this elliptic curve, if it can be determined. | 460,602 |
def rank(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Return the rank of this elliptic curve, if it can be determined. | def rank(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Return the rank of this elliptic curve, if it can be determined. | 460,603 |
def rank(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Return the rank of this elliptic curve, if it can be determined. | def rank(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Return the rank of this elliptic curve, if it can be determined. | 460,604 |
def rank(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Return the rank of this elliptic curve, if it can be determined. | def rank(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Return the rank of this elliptic curve, if it can be determined. | 460,605 |
def rank(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Return the rank of this elliptic curve, if it can be determined. | def rank(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Return the rank of this elliptic curve, if it can be determined. | 460,606 |
def rank(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Return the rank of this elliptic curve, if it can be determined. | def rank(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Return the rank of this elliptic curve, if it can be determined. | 460,607 |
def gens(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns some generators of this elliptic curve. Check rank or rank_bound to verify the number of generators. | def gens(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns some generators of this elliptic curve. Check rank or rank_bound to verify the number of generators. | 460,608 |
def gens(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns some generators of this elliptic curve. Check rank or rank_bound to verify the number of generators. | def gens(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns some generators of this elliptic curve. Check rank or rank_bound to verify the number of generators. | 460,609 |
def gens(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns some generators of this elliptic curve. Check rank or rank_bound to verify the number of generators. | def gens(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns some generators of this elliptic curve. Check rank or rank_bound to verify the number of generators. | 460,610 |
def gens(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns some generators of this elliptic curve. Check rank or rank_bound to verify the number of generators. | def gens(self,verbose=0, lim1=5, lim3=50, limtriv=10, maxprob=20, limbigprime=30): r""" Returns some generators of this elliptic curve. Check rank or rank_bound to verify the number of generators. | 460,611 |
sage: def naive_height(P): | sage: def naive_height(P): | 460,612 |
def crt(a,b,m=None,n=None): r""" Returns a solution to a Chinese Remainder Theorem problem. INPUT: - ``a``, ``b`` - two residues (elements of some ring for which extended gcd is available), or two lists, one of residues and one of moduli. - ``m``, ``n`` - two moduli, or None. OUTPUT: If ``m``, ``n`` are not None, ... | def crt(a,b,m=None,n=None): r""" Returns a solution to a Chinese Remainder Theorem problem. INPUT: - ``a``, ``b`` - two residues (elements of some ring for which extended gcd is available), or two lists, one of residues and one of moduli. - ``m``, ``n`` - (default: ``None``) two moduli, or ``None``. OUTPUT: If ``m... | 460,613 |
def crt(a,b,m=None,n=None): r""" Returns a solution to a Chinese Remainder Theorem problem. INPUT: - ``a``, ``b`` - two residues (elements of some ring for which extended gcd is available), or two lists, one of residues and one of moduli. - ``m``, ``n`` - two moduli, or None. OUTPUT: If ``m``, ``n`` are not None, ... | def crt(a,b,m=None,n=None): r""" Returns a solution to a Chinese Remainder Theorem problem. INPUT: - ``a``, ``b`` - two residues (elements of some ring for which extended gcd is available), or two lists, one of residues and one of moduli. - ``m``, ``n`` - two moduli, or None. OUTPUT: If ``m``, ``n`` are not ``None... | 460,614 |
def crt(a,b,m=None,n=None): r""" Returns a solution to a Chinese Remainder Theorem problem. INPUT: - ``a``, ``b`` - two residues (elements of some ring for which extended gcd is available), or two lists, one of residues and one of moduli. - ``m``, ``n`` - two moduli, or None. OUTPUT: If ``m``, ``n`` are not None, ... | def crt(a,b,m=None,n=None): r""" Returns a solution to a Chinese Remainder Theorem problem. INPUT: - ``a``, ``b`` - two residues (elements of some ring for which extended gcd is available), or two lists, one of residues and one of moduli. - ``m``, ``n`` - two moduli, or None. OUTPUT: If ``m``, ``n`` are not None, ... | 460,615 |
def crt(a,b,m=None,n=None): r""" Returns a solution to a Chinese Remainder Theorem problem. INPUT: - ``a``, ``b`` - two residues (elements of some ring for which extended gcd is available), or two lists, one of residues and one of moduli. - ``m``, ``n`` - two moduli, or None. OUTPUT: If ``m``, ``n`` are not None, ... | def crt(a,b,m=None,n=None): r""" Returns a solution to a Chinese Remainder Theorem problem. INPUT: - ``a``, ``b`` - two residues (elements of some ring for which extended gcd is available), or two lists, one of residues and one of moduli. - ``m``, ``n`` - two moduli, or None. OUTPUT: If ``m``, ``n`` are not None, ... | 460,616 |
def crt(a,b,m=None,n=None): r""" Returns a solution to a Chinese Remainder Theorem problem. INPUT: - ``a``, ``b`` - two residues (elements of some ring for which extended gcd is available), or two lists, one of residues and one of moduli. - ``m``, ``n`` - two moduli, or None. OUTPUT: If ``m``, ``n`` are not None, ... | def crt(a,b,m=None,n=None): r""" Returns a solution to a Chinese Remainder Theorem problem. INPUT: - ``a``, ``b`` - two residues (elements of some ring for which extended gcd is available), or two lists, one of residues and one of moduli. - ``m``, ``n`` - two moduli, or None. OUTPUT: If ``m``, ``n`` are not None, ... | 460,617 |
def crt(a,b,m=None,n=None): r""" Returns a solution to a Chinese Remainder Theorem problem. INPUT: - ``a``, ``b`` - two residues (elements of some ring for which extended gcd is available), or two lists, one of residues and one of moduli. - ``m``, ``n`` - two moduli, or None. OUTPUT: If ``m``, ``n`` are not None, ... | def crt(a,b,m=None,n=None): r""" Returns a solution to a Chinese Remainder Theorem problem. INPUT: - ``a``, ``b`` - two residues (elements of some ring for which extended gcd is available), or two lists, one of residues and one of moduli. - ``m``, ``n`` - two moduli, or None. OUTPUT: If ``m``, ``n`` are not None, ... | 460,618 |
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:: | 460,619 |
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:: | 460,620 |
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:: | 460,621 |
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:: | 460,622 |
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:: | 460,623 |
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:: | 460,624 |
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:: | 460,625 |
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:: | 460,626 |
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:: | 460,627 |
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:: | 460,628 |
def _limit_latex_(*args): 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(x) = function('f',x) sage: _limit_latex_(f(x), x, a) '\\lim_{x \\to a}\\, f\\left(x\\right)' AUTHORS: - Golam Mortuza Hossain (20... | 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(x) = function('f',x) sage: _limit_latex_(f(x), x, a) '\\lim_{x \\to a}\\, f\\left(x\\right)' AUTHORS: - Golam Mortuza Hos... | 460,629 |
def _limit_latex_(*args): 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(x) = function('f',x) sage: _limit_latex_(f(x), x, a) '\\lim_{x \\to a}\\, f\\left(x\\right)' AUTHORS: - Golam Mortuza Hossain (20... | def _limit_latex_(*args): 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)' AUTHORS: - Golam Mortuza Hossain (2009-... | 460,630 |
def _limit_latex_(*args): 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(x) = function('f',x) sage: _limit_latex_(f(x), x, a) '\\lim_{x \\to a}\\, f\\left(x\\right)' AUTHORS: - Golam Mortuza Hossain (20... | def _limit_latex_(*args): 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(x) = function('f',x) sage: _limit_latex_(f(x), x, a) '\\lim_{x \\to a}\\, f\\left(x\\right)' AUTHORS: - Golam Mortuza Hossain (20... | 460,631 |
def _integrate_latex_(*args): r""" Return LaTeX expression for integration of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _integrate_latex_ sage: var('x,a,b') (x, a, b) sage: f(x) = function('f',x) sage: _integrate_latex_(f(x),x) '\\int f\\left(x\\right)\\,{d x}' sage: _integrate_latex_(f... | def _integrate_latex_(self, f, x, *args): r""" Return LaTeX expression for integration of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _integrate_latex_ sage: var('x,a,b') (x, a, b) sage: f(x) = function('f',x) sage: _integrate_latex_(f(x),x) '\\int f\\left(x\\right)\\,{d x}' sage: _integr... | 460,632 |
def _integrate_latex_(*args): r""" Return LaTeX expression for integration of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _integrate_latex_ sage: var('x,a,b') (x, a, b) sage: f(x) = function('f',x) sage: _integrate_latex_(f(x),x) '\\int f\\left(x\\right)\\,{d x}' sage: _integrate_latex_(f... | def _integrate_latex_(*args): r""" Return LaTeX expression for integration of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _integrate_latex_ sage: var('x,a,b') (x, a, b) sage: f = function('f',x) sage: _integrate_latex_(0,f,x) '\\int f\\left(x\\right)\\,{d x}' sage: _integrate_latex_(f(x),... | 460,633 |
def _integrate_latex_(*args): r""" Return LaTeX expression for integration of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _integrate_latex_ sage: var('x,a,b') (x, a, b) sage: f(x) = function('f',x) sage: _integrate_latex_(f(x),x) '\\int f\\left(x\\right)\\,{d x}' sage: _integrate_latex_(f... | def _integrate_latex_(*args): r""" Return LaTeX expression for integration of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _integrate_latex_ sage: var('x,a,b') (x, a, b) sage: f(x) = function('f',x) sage: _integrate_latex_(f(x),x) '\\int f\\left(x\\right)\\,{d x}' sage: _integrate_latex_(0... | 460,634 |
def _integrate_latex_(*args): r""" Return LaTeX expression for integration of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _integrate_latex_ sage: var('x,a,b') (x, a, b) sage: f(x) = function('f',x) sage: _integrate_latex_(f(x),x) '\\int f\\left(x\\right)\\,{d x}' sage: _integrate_latex_(f... | def _integrate_latex_(*args): r""" Return LaTeX expression for integration of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _integrate_latex_ sage: var('x,a,b') (x, a, b) sage: f(x) = function('f',x) sage: _integrate_latex_(f(x),x) '\\int f\\left(x\\right)\\,{d x}' sage: _integrate_latex_(f... | 460,635 |
def _integrate_latex_(*args): r""" Return LaTeX expression for integration of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _integrate_latex_ sage: var('x,a,b') (x, a, b) sage: f(x) = function('f',x) sage: _integrate_latex_(f(x),x) '\\int f\\left(x\\right)\\,{d x}' sage: _integrate_latex_(f... | def _integrate_latex_(*args): r""" Return LaTeX expression for integration of a symbolic function. EXAMPLES:: sage: from sage.calculus.calculus import _integrate_latex_ sage: var('x,a,b') (x, a, b) sage: f(x) = function('f',x) sage: _integrate_latex_(f(x),x) '\\int f\\left(x\\right)\\,{d x}' sage: _integrate_latex_(f... | 460,636 |
def _laplace_latex_(*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(t) = function('f',t) sage: _laplace_latex_(f(t),t,s) '\\mathcal{L}\\left(f\\left(t\\right), t, s\\right)' AUTHORS:... | 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(t) = function('f',t) sage: _laplace_latex_(f(t),t,s) '\\mathcal{L}\\left(f\\left(t\\right), t, s\\right)' AU... | 460,637 |
def _laplace_latex_(*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(t) = function('f',t) sage: _laplace_latex_(f(t),t,s) '\\mathcal{L}\\left(f\\left(t\\right), t, s\\right)' AUTHORS:... | def _laplace_latex_(*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)' AUTHORS: - ... | 460,638 |
def _inverse_laplace_latex_(*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(s) = function('F',s) sage: _inverse_laplace_latex_(F(s),s,t) '\\mathcal{L}^{-1}\\left(F\\le... | 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(s) = function('F',s) sage: _inverse_laplace_latex_(F(s),s,t) '\\mathcal{L}^{-1}\\left... | 460,639 |
def _inverse_laplace_latex_(*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(s) = function('F',s) sage: _inverse_laplace_latex_(F(s),s,t) '\\mathcal{L}^{-1}\\left(F\\le... | def _inverse_laplace_latex_(*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\\left(s... | 460,640 |
def integral(f, *args, **kwds): r""" The integral of `f`. EXAMPLES:: sage: integral(sin(x), x) -cos(x) sage: integral(sin(x)^2, x, pi, 123*pi/2) 121/4*pi sage: integral( sin(x), x, 0, pi) 2 We integrate a symbolic function:: sage: f(x,y,z) = x*y/z + sin(z) sage: integral(f, z) (x, y, z) |--> x*y*log(z) - cos(z) ::... | def integral(f, *args, **kwds): r""" The integral of `f`. EXAMPLES:: sage: integral(sin(x), x) -cos(x) sage: integral(sin(x)^2, x, pi, 123*pi/2) 121/4*pi sage: integral( sin(x), x, 0, pi) 2 We integrate a symbolic function:: sage: f(x,y,z) = x*y/z + sin(z) sage: integral(f, z) (x, y, z) |--> x*y*log(z) - cos(z) ::... | 460,641 |
sage: def is_4regular(G): | sage: def is_4regular(G): | 460,642 |
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`. | 460,643 |
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`. | 460,644 |
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`. | 460,645 |
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... | 460,646 |
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`. | 460,647 |
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>`_. INPUT: | 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>`_. INPUT: | 460,648 |
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>`_. INPUT: | 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>`_. INPUT: | 460,649 |
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>`_. INPUT: | 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>`_. INPUT: | 460,650 |
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... | 460,651 |
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... | 460,652 |
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>`_. | 460,653 |
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>`_. | 460,654 |
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>`_. | 460,655 |
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)>`_. INPUT: | 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)>`_. INPUT: | 460,656 |
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)>`_. INPUT: | 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)>`_. INPUT: | 460,657 |
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)>`_. INPUT: | 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)>`_. INPUT: | 460,658 |
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)>`_. INPUT: | 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)>`_. INPUT: | 460,659 |
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)>`_. INPUT: | 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)>`_. INPUT: | 460,660 |
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)>`_. INPUT: | 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)>`_. INPUT: | 460,661 |
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)>`_. INPUT: | 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)>`_. INPUT: | 460,662 |
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)>`_. INPUT: | 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)>`_. INPUT: | 460,663 |
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)>`_. INPUT: | 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)>`_. INPUT: | 460,664 |
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. | 460,665 |
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. | 460,666 |
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. | 460,667 |
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. | 460,668 |
def _render_on_subplot(self, subplot): """ TESTS: | def _render_on_subplot(self, subplot): """ TESTS: | 460,669 |
def _render_on_subplot(self, subplot): """ TESTS: | def _render_on_subplot(self, subplot): """ TESTS: | 460,670 |
def _render_on_subplot(self, subplot): """ TESTS: | def _render_on_subplot(self, subplot): """ TESTS: | 460,671 |
def contour_plot(f, xrange, yrange, **options): r""" ``contour_plot`` takes a function of two variables, `f(x,y)` and plots contour lines of the function over the specified ``xrange`` and ``yrange`` as demonstrated below. ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)`` INPUT: - ``f`` -- a function of two variab... | def contour_plot(f, xrange, yrange, **options): r""" ``contour_plot`` takes a function of two variables, `f(x,y)` and plots contour lines of the function over the specified ``xrange`` and ``yrange`` as demonstrated below. ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)`` INPUT: - ``f`` -- a function of two variab... | 460,672 |
def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth,**options): r""" ``region_plot`` takes a boolean function of two variables, `f(x,y)` and plots the region where f is True over the specified ``xrange`` and ``yrange`` as demonstrated below. ``region_plot(f, (xmin, xmax),... | def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth,**options): r""" ``region_plot`` takes a boolean function of two variables, `f(x,y)` and plots the region where f is True over the specified ``xrange`` and ``yrange`` as demonstrated below. ``region_plot(f, (xmin, xmax),... | 460,673 |
def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth,**options): r""" ``region_plot`` takes a boolean function of two variables, `f(x,y)` and plots the region where f is True over the specified ``xrange`` and ``yrange`` as demonstrated below. ``region_plot(f, (xmin, xmax),... | def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth,**options): r""" ``region_plot`` takes a boolean function of two variables, `f(x,y)` and plots the region where f is True over the specified ``xrange`` and ``yrange`` as demonstrated below. ``region_plot(f, (xmin, xmax),... | 460,674 |
def random_element(self, prec, bound=None): r""" Return a random power series. INPUT: - ``prec`` - an integer - ``bound`` - an integer (default: None, which tries to spread choice across ring, if implemented) OUTPUT: - ``power series`` - a power series such that the coefficient of `x^i`, for `i` up to ``degr... | def random_element(self, prec=None, *args, **kwds): r""" Return a random power series. INPUT: - ``prec`` - an integer - ``bound`` - an integer (default: None, which tries to spread choice across ring, if implemented) OUTPUT: - ``power series`` - a power series such that the coefficient of `x^i`, for `i` up t... | 460,675 |
def random_element(self, prec, bound=None): r""" Return a random power series. INPUT: - ``prec`` - an integer - ``bound`` - an integer (default: None, which tries to spread choice across ring, if implemented) OUTPUT: - ``power series`` - a power series such that the coefficient of `x^i`, for `i` up to ``degr... | def random_element(self, prec, bound=None): r""" Return a random power series. INPUT: - ``prec`` - an integer - ``bound`` - an integer (default: None, which tries to spread choice across ring, if implemented) OUTPUT: - ``power series`` - a power series such ... | 460,676 |
def random_element(self, prec, bound=None): r""" Return a random power series. INPUT: - ``prec`` - an integer - ``bound`` - an integer (default: None, which tries to spread choice across ring, if implemented) OUTPUT: - ``power series`` - a power series such that the coefficient of `x^i`, for `i` up to ``degr... | def random_element(self, prec, bound=None): r""" Return a random power series. INPUT: - ``prec`` - Integer specifying precision of output (default: default precision of self) - ``*args, **kwds`` - Passed on to the ``random_element`` method for the base ring OUTPUT: - ``power series`` - a power series such that... | 460,677 |
def random_element(self, prec, bound=None): r""" Return a random power series. INPUT: - ``prec`` - an integer - ``bound`` - an integer (default: None, which tries to spread choice across ring, if implemented) OUTPUT: - ``power series`` - a power series such that the coefficient of `x^i`, for `i` up to ``degr... | def random_element(self, prec, bound=None): r""" Return a random power series. INPUT: - ``prec`` - an integer - ``bound`` - an integer (default: None, which tries to spread choice across ring, if implemented) OUTPUT: - Power series with precision ``prec`` whose coefficients are random elements from the base r... | 460,678 |
def random_element(self, prec, bound=None): r""" Return a random power series. INPUT: - ``prec`` - an integer - ``bound`` - an integer (default: None, which tries to spread choice across ring, if implemented) OUTPUT: - ``power series`` - a power series such that the coefficient of `x^i`, for `i` up to ``degr... | def random_element(self, prec, bound=None): r""" Return a random power series. INPUT: - ``prec`` - an integer - ``bound`` - an integer (default: None, which tries to spread choice across ring, if implemented) OUTPUT: - ``power series`` - a power series such that the coefficient of `x^i`, for `i` up to ``degr... | 460,679 |
def random_element(self, prec, bound=None): r""" Return a random power series. INPUT: - ``prec`` - an integer - ``bound`` - an integer (default: None, which tries to spread choice across ring, if implemented) OUTPUT: - ``power series`` - a power series such that the coefficient of `x^i`, for `i` up to ``degr... | def random_element(self, prec, bound=None): r""" Return a random power series. INPUT: - ``prec`` - an integer - ``bound`` - an integer (default: None, which tries to spread choice across ring, if implemented) OUTPUT: - ``power series`` - a power series such that the coefficient of `x^i`, for `i` up to ``degr... | 460,680 |
def random_element(self, prec, bound=None): r""" Return a random power series. INPUT: - ``prec`` - an integer - ``bound`` - an integer (default: None, which tries to spread choice across ring, if implemented) OUTPUT: - ``power series`` - a power series such that the coefficient of `x^i`, for `i` up to ``degr... | def random_element(self, prec=None, *args, **kwds): r""" Return a random power series. INPUT: - ``prec`` - an integer - ``bound`` - an integer (default: None, which tries to spread choice across ring, if implemented) OUTPUT: - ``power series`` - a power series such that the coefficient of `x^i`, for `i` up t... | 460,681 |
def random_element(self, prec, bound=None): r""" Return a random power series. INPUT: - ``prec`` - an integer - ``bound`` - an integer (default: None, which tries to spread choice across ring, if implemented) OUTPUT: - ``power series`` - a power series such that the coefficient of `x^i`, for `i` up to ``degr... | def random_element(self, prec, bound=None): r""" Return a random power series. INPUT: - ``prec`` - an integer - ``bound`` - an integer (default: None, which tries to spread choice across ring, if implemented) OUTPUT: - ``power series`` - a power series such ... | 460,682 |
def random_element(self, prec, bound=None): r""" Return a random power series. INPUT: - ``prec`` - an integer - ``bound`` - an integer (default: None, which tries to spread choice across ring, if implemented) OUTPUT: - ``power series`` - a power series such that the coefficient of `x^i`, for `i` up to ``degr... | def random_element(self, prec, bound=None): r""" Return a random power series. INPUT: - ``prec`` - Integer specifying precision of output (default: default precision of self) - ``*args, **kwds`` - Passed on to the ``random_element`` method for the base ring OUTPUT: - ``power series`` - a power series such that... | 460,683 |
def random_element(self, prec, bound=None): r""" Return a random power series. INPUT: - ``prec`` - an integer - ``bound`` - an integer (default: None, which tries to spread choice across ring, if implemented) OUTPUT: - ``power series`` - a power series such that the coefficient of `x^i`, for `i` up to ``degr... | def random_element(self, prec, bound=None): r""" Return a random power series. INPUT: - ``prec`` - an integer - ``bound`` - an integer (default: None, which tries to spread choice across ring, if implemented) OUTPUT: - Power series with precision ``prec`` whose coefficients are random elements from the base r... | 460,684 |
def random_element(self, prec, bound=None): r""" Return a random power series. INPUT: - ``prec`` - an integer - ``bound`` - an integer (default: None, which tries to spread choice across ring, if implemented) OUTPUT: - ``power series`` - a power series such that the coefficient of `x^i`, for `i` up to ``degr... | def random_element(self, prec, bound=None): r""" Return a random power series. INPUT: - ``prec`` - an integer - ``bound`` - an integer (default: None, which tries to spread choice across ring, if implemented) OUTPUT: - ``power series`` - a power series such that the coefficient of `x^i`, for `i` up to ``degr... | 460,685 |
def random_element(self, prec, bound=None): r""" Return a random power series. INPUT: - ``prec`` - an integer - ``bound`` - an integer (default: None, which tries to spread choice across ring, if implemented) OUTPUT: - ``power series`` - a power series such that the coefficient of `x^i`, for `i` up to ``degr... | def random_element(self, prec, bound=None): r""" Return a random power series. INPUT: - ``prec`` - an integer - ``bound`` - an integer (default: None, which tries to spread choice across ring, if implemented) OUTPUT: - ``power series`` - a power series such that the coefficient of `x^i`, for `i` up to ``degr... | 460,686 |
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... | 460,687 |
def __init__(self, parent, value, check=True): """ Create element of a finite field. EXAMPLES:: sage: from sage.rings.finite_rings.finite_field_ext_pari import FiniteField_ext_pari sage: k = FiniteField_ext_pari(9,'a') sage: a = k(11); a 2 sage: a.parent() Finite Field in a of size 3^2 sage: V = k.vector_space(); v =... | def __init__(self, parent, value, check=True): """ Create element of a finite field. EXAMPLES:: sage: from sage.rings.finite_rings.finite_field_ext_pari import FiniteField_ext_pari sage: k = FiniteField_ext_pari(9,'a') sage: a = k(11); a 2 sage: a.parent() Finite Field in a of size 3^2 sage: V = k.vector_space(); v =... | 460,688 |
def factorial(n, algorithm='gmp'): r""" Compute the factorial of `n`, which is the product `1\cdot 2\cdot 3 \cdots (n-1)\cdot n`. INPUT: - ``n`` - an integer - ``algorithm`` - string (default: 'gmp') - ``'gmp'`` - use the GMP C-library factorial function - ``'pari'`` - use PARI's factorial function OUTPUT: an... | def factorial(n, algorithm='gmp'): r""" Compute the factorial of `n`, which is the product `1\cdot 2\cdot 3 \cdots (n-1)\cdot n`. INPUT: - ``n`` - an integer - ``algorithm`` - string (default: 'gmp'): - ``'gmp'`` - use the GMP C-library factorial function - ``'pari'`` - use PARI's factorial function OUTPUT: a... | 460,689 |
def factorial(n, algorithm='gmp'): r""" Compute the factorial of `n`, which is the product `1\cdot 2\cdot 3 \cdots (n-1)\cdot n`. INPUT: - ``n`` - an integer - ``algorithm`` - string (default: 'gmp') - ``'gmp'`` - use the GMP C-library factorial function - ``'pari'`` - use PARI's factorial function OUTPUT: an... | def factorial(n, algorithm='gmp'): r""" Compute the factorial of `n`, which is the product `1\cdot 2\cdot 3 \cdots (n-1)\cdot n`. INPUT: - ``n`` - an integer - ``algorithm`` - string (default: 'gmp') - ``'gmp'`` - use the GMP C-library factorial function - ``'pari'`` - use PARI's factorial function OUTPUT: an... | 460,690 |
def crt(a,b,m=None,n=None): r""" Use the Chinese Remainder Theorem to find some `x` such that `x=a \bmod m` and `x=b \bmod n`. Note that `x` is only well-defined modulo `m\*n`. EXAMPLES:: sage: crt(2, 1, 3, 5) -4 sage: crt(13,20,100,301) -2087 You can also use upper case:: sage: c = CRT(2,3, 3, 5); c 8 sage: c % 3 ... | def crt(a,b,m=None,n=None): r""" Use the Chinese Remainder Theorem to find some `x` such that `x=a \bmod m` and `x=b \bmod n`. Note that `x` is only well-defined modulo `m*n`. EXAMPLES:: sage: crt(2, 1, 3, 5) -4 sage: crt(13,20,100,301) -2087 You can also use upper case:: sage: c = CRT(2,3, 3, 5); c 8 sage: c % 3 =... | 460,691 |
def matrix(*args, **kwds): """ Create a matrix. INPUT: The matrix command takes the entries of a matrix, optionally preceded by a ring and the dimensions of the matrix, and returns a matrix. The entries of a matrix can be specified as a flat list of elements, a list of lists (i.e., a list of rows), a list of Sage vec... | def matrix(*args, **kwds): """ Create a matrix. INPUT: The matrix command takes the entries of a matrix, optionally preceded by a ring and the dimensions of the matrix, and returns a matrix. The entries of a matrix can be specified as a flat list of elements, a list of lists (i.e., a list of rows), a list of Sage vec... | 460,692 |
def update(self): """ Updates some properties from ``curve``. | def update(self): """ Updates some properties from ``curve``. | 460,693 |
sage: def foo(use_database): | sage: def foo(use_database): | 460,694 |
def induced_subgraph_search(self, G): r""" Returns an induced copy of `G` in self. | def subgraph_search(self, G, induced=False): r""" Returns an induced copy of `G` in self. | 460,695 |
def induced_subgraph_search(self, G): r""" Returns an induced copy of `G` in self. | def induced_subgraph_search(self, G): r""" Returns an induced copy of `G` in self. | 460,696 |
def induced_subgraph_search(self, G): r""" Returns an induced copy of `G` in self. | def induced_subgraph_search(self, G): r""" Returns an induced copy of `G` in self. | 460,697 |
def induced_subgraph_search(self, G): r""" Returns an induced copy of `G` in self. | def induced_subgraph_search(self, G): r""" Returns an induced copy of `G` in self. | 460,698 |
def induced_subgraph_search(self, G): r""" Returns an induced copy of `G` in self. | def induced_subgraph_search(self, G): r""" Returns an induced copy of `G` in self. | 460,699 |
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