bugged stringlengths 4 228k | fixed stringlengths 0 96.3M | __index_level_0__ int64 0 481k |
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def _read_in_file_command(self, filename): """ EXAMPLES: sage: from sage.misc.misc import tmp_filename sage: filename = tmp_filename() sage: f = open(filename, "w") sage: f.write("Hello") sage: f.close() sage: command = macaulay2._read_in_file_command(filename) sage: macaulay2.eval(command) #optional Hello sage: impor... | def _read_in_file_command(self, filename): """ Load and *execute* the content of ``filename`` in Macaulay2. :param filename: the name of the file to be loaded and executed. :type filename: string :returns: Macaulay2 command loading and executing commands in ``filename``, that is, ``'load "filename"'``. :rtype: string ... | 460,300 |
def _read_in_file_command(self, filename): """ EXAMPLES: sage: from sage.misc.misc import tmp_filename sage: filename = tmp_filename() sage: f = open(filename, "w") sage: f.write("Hello") sage: f.close() sage: command = macaulay2._read_in_file_command(filename) sage: macaulay2.eval(command) #optional Hello sage: impor... | def _read_in_file_command(self, filename): """ EXAMPLES: sage: from sage.misc.misc import tmp_filename sage: filename = tmp_filename() sage: f = open(filename, "w") sage: f.write("sage_test = 7;") sage: f.close() sage: command = macaulay2._read_in_file_command(filename) sage: macaulay2.eval(command) #optional Hello sa... | 460,301 |
def _read_in_file_command(self, filename): """ EXAMPLES: sage: from sage.misc.misc import tmp_filename sage: filename = tmp_filename() sage: f = open(filename, "w") sage: f.write("Hello") sage: f.close() sage: command = macaulay2._read_in_file_command(filename) sage: macaulay2.eval(command) #optional Hello sage: impor... | def _read_in_file_command(self, filename): """ EXAMPLES: sage: from sage.misc.misc import tmp_filename sage: filename = tmp_filename() sage: f = open(filename, "w") sage: f.write("Hello") sage: f.close() sage: command = macaulay2._read_in_file_command(filename) sage: macaulay2.eval(command) #optional sage: macaulay2.e... | 460,302 |
def _read_in_file_command(self, filename): """ EXAMPLES: sage: from sage.misc.misc import tmp_filename sage: filename = tmp_filename() sage: f = open(filename, "w") sage: f.write("Hello") sage: f.close() sage: command = macaulay2._read_in_file_command(filename) sage: macaulay2.eval(command) #optional Hello sage: impor... | def _read_in_file_command(self, filename): """ EXAMPLES: sage: from sage.misc.misc import tmp_filename sage: filename = tmp_filename() sage: f = open(filename, "w") sage: f.write("Hello") sage: f.close() sage: command = macaulay2._read_in_file_command(filename) sage: macaulay2.eval(command) #optional Hello sage: impor... | 460,303 |
def process_dollars(s): r"""nodetex Replace dollar signs with backticks. More precisely, do a regular expression search. Replace a plain dollar sign ($) by a backtick (`). Replace an escaped dollar sign (\$) by a dollar sign ($). Don't change a dollar sign preceded or followed by a backtick (`$ or $`), because of s... | def process_dollars(s): r"""nodetex Replace dollar signs with backticks. More precisely, do a regular expression search. Replace a plain dollar sign ($) by a backtick (`). Replace an escaped dollar sign (\\$) by a dollar sign ($). Don't change a dollar sign preceded or followed by a backtick (\`$ or \$`), because o... | 460,304 |
def process_dollars(s): r"""nodetex Replace dollar signs with backticks. More precisely, do a regular expression search. Replace a plain dollar sign ($) by a backtick (`). Replace an escaped dollar sign (\$) by a dollar sign ($). Don't change a dollar sign preceded or followed by a backtick (`$ or $`), because of s... | def process_dollars(s): r"""nodetex Replace dollar signs with backticks. More precisely, do a regular expression search. Replace a plain dollar sign ($) by a backtick (`). Replace an escaped dollar sign (\$) by a dollar sign ($). Don't change a dollar sign preceded or followed by a backtick (`$ or $`), because of s... | 460,305 |
def process_dollars(s): r"""nodetex Replace dollar signs with backticks. More precisely, do a regular expression search. Replace a plain dollar sign ($) by a backtick (`). Replace an escaped dollar sign (\$) by a dollar sign ($). Don't change a dollar sign preceded or followed by a backtick (`$ or $`), because of s... | def process_dollars(s): r"""nodetex Replace dollar signs with backticks. More precisely, do a regular expression search. Replace a plain dollar sign ($) by a backtick (`). Replace an escaped dollar sign (\$) by a dollar sign ($). Don't change a dollar sign preceded or followed by a backtick (`$ or $`), because of s... | 460,306 |
def process_mathtt(s, embedded=False): r"""nodetex Replace \mathtt{BLAH} with either \verb|BLAH| (in the notebook) or BLAH (from the command line). INPUT: - ``s`` - string, in practice a docstring - ``embedded`` - boolean (optional, default False) This function is called by :func:`format`, and if in the notebook, it... | def process_mathtt(s, embedded=False): r"""nodetex Replace \\mathtt{BLAH} with either \\verb|BLAH| (in the notebook) or BLAH (from the command line). INPUT: - ``s`` - string, in practice a docstring - ``embedded`` - boolean (optional, default False) This function is called by :func:`format`, and if in the notebook, ... | 460,307 |
... def __reduce__(self): | ... def __reduce__(self): | 460,308 |
def __classcall_private__(cls, fam, facade=True, keepkey=False): # was *args, **options): """ Normalization of arguments; see :cls:`UniqueRepresentation`. | def __classcall_private__(cls, fam, facade=True, keepkey=False): # was *args, **options): """ Normalization of arguments; see :cls:`UniqueRepresentation`. | 460,309 |
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 ... | 460,310 |
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... | 460,311 |
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... | 460,312 |
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... | 460,313 |
def hom(self, im_gens, codomain=None, check=True): """ Homomorphism defined by giving the images of ``self.gens()`` in some fixed fg R-module. .. note :: We do not assume that the generators given by ``self.gens()`` are the same as the Smith form generators, since this may not be true for a general derived class. IN... | def hom(self, im_gens, codomain=None, check=True): """ Homomorphism defined by giving the images of ``self.gens()`` in some fixed fg R-module. .. note :: We do not assume that the generators given by ``self.gens()`` are the same as the Smith form generators, since this may not be true for a general derived class. IN... | 460,314 |
def hom(self, im_gens, codomain=None, check=True): """ Homomorphism defined by giving the images of ``self.gens()`` in some fixed fg R-module. .. note :: We do not assume that the generators given by ``self.gens()`` are the same as the Smith form generators, since this may not be true for a general derived class. IN... | def hom(self, im_gens, codomain=None, check=True): """ Homomorphism defined by giving the images of ``self.gens()`` in some fixed fg R-module. .. note :: We do not assume that the generators given by ``self.gens()`` are the same as the Smith form generators, since this may not be true for a general derived class. IN... | 460,315 |
def __init__(self, point, r, angle, options): """ Initializes base class Disk. | def __init__(self, point, r, angle, options): """ Initializes base class Disk. | 460,316 |
def get_minmax_data(self): """ Returns a dictionary with the bounding box data. | def get_minmax_data(self): """ Returns a dictionary with the bounding box data. | 460,317 |
def _allowed_options(self): """ Return the allowed options for the Disk class. | def _allowed_options(self): """ Return the allowed options for the Disk class. | 460,318 |
def _repr_(self): """ String representation of Disk primitive. | def _repr_(self): """ String representation of Disk primitive. | 460,319 |
def plot3d(self, z=0, **kwds): """ Plots a 2D disk (actually a 52-gon) in 3D, with default height zero. | def plot3d(self, z=0, **kwds): """ Plots a 2D disk (actually a 52-gon) in 3D, with default height zero. | 460,320 |
def module_morphism(self, on_basis = None, diagonal = None, triangular = None, **keywords): r""" Constructs morphisms by linearity | def module_morphism(self, on_basis = None, diagonal = None, triangular = None, **keywords): r""" Constructs morphisms by linearity | 460,321 |
def leading_item(self, cmp=None): r""" Returns the pair ``(k, c)`` where ``c`` * (the basis elt. indexed by ``k``) is the leading term of ``self``. | def leading_item(self, cmp=None): r""" Returns the pair ``(k, c)`` where ``c`` * (the basis elt. indexed by ``k``) is the leading term of ``self``. | 460,322 |
def leading_monomial(self, cmp=None): r""" Returns the leading monomial of ``self``. | def leading_monomial(self, cmp=None): r""" Returns the leading monomial of ``self``. | 460,323 |
def leading_coefficient(self, cmp=None): r""" Returns the leading coefficient of ``self``. | def leading_coefficient(self, cmp=None): r""" Returns the leading coefficient of ``self``. | 460,324 |
def leading_term(self, cmp=None): r""" Returns the leading term of ``self``. | def leading_term(self, cmp=None): r""" Returns the leading term of ``self``. | 460,325 |
def trailing_item(self, cmp=None): r""" Returns the pair ``(c, k)`` where ``c*self.parent().monomial(k)`` is the trailing term of ``self``. | def trailing_item(self, cmp=None): r""" Returns the pair ``(c, k)`` where ``c*self.parent().monomial(k)`` is the trailing term of ``self``. | 460,326 |
def trailing_monomial(self, cmp=None): r""" Returns the trailing monomial of ``self``. | def trailing_monomial(self, cmp=None): r""" Returns the trailing monomial of ``self``. | 460,327 |
def trailing_coefficient(self, cmp=None): r""" Returns the trailing coefficient of ``self``. | def trailing_coefficient(self, cmp=None): r""" Returns the trailing coefficient of ``self``. | 460,328 |
def trailing_term(self, cmp=None): r""" Returns the trailing term of ``self``. | def trailing_term(self, cmp=None): r""" Returns the trailing term of ``self``. | 460,329 |
def extra_super_categories(self): """ EXAMPLES:: | def extra_super_categories(self): """ EXAMPLES:: | 460,330 |
sage: def phi_on_basis(i): return Y.monomial(abs(i)) | sage: def phi_on_basis(i): return Y.monomial(abs(i)) | 460,331 |
sage: def phi_on_basis(i): return Y.monomial(abs(i)) | sage: def phi_on_basis(i): return Y.monomial(abs(i)) | 460,332 |
sage: def phi_on_basis(i): return Y.monomial(abs(i)) | sage: def phi_on_basis(i): return Y.monomial(abs(i)) | 460,333 |
def _test_triangular(self, **options): """ Tests that ``self`` is actually triangular | def _test_triangular(self, **options): """ Tests that ``self`` is actually triangular | 460,334 |
def _test_triangular(self, **options): """ Tests that ``self`` is actually triangular | def _test_triangular(self, **options): """ Tests that ``self`` is actually triangular | 460,335 |
def _test_triangular(self, **options): """ Tests that ``self`` is actually triangular | def _test_triangular(self, **options): """ Tests that ``self`` is actually triangular | 460,336 |
def _test_triangular(self, **options): """ Tests that ``self`` is actually triangular | def _test_triangular(self, **options): """ Tests that ``self`` is actually triangular | 460,337 |
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... | 460,338 |
def eval(self, Vobj): r""" Evaluates the left hand side `A\vec{x}+b` on the given vertex/ray/line. NOTES: * Evaluating on a vertex returns `A\vec{x}+b` * Evaluating on a ray returns `A\vec{r}`. Only the sign or whether it is zero is meaningful. * Evaluating on a line returns `A\vec{l}`. Only whether it is zero or not... | def eval(self, Vobj): r""" Evaluates the left hand side `A\vec{x}+b` on the given vertex/ray/line. NOTES: * Evaluating on a vertex returns `A\vec{x}+b` * Evaluating on a ray returns `A\vec{r}`. Only the sign or whether it is zero is meaningful. * Evaluating on a line returns `A\vec{l}`. Only whether it is zero or not... | 460,339 |
def is_inequality(self): """ Returns True since this is, by construction, an inequality. | def is_inequality(self): """ Returns True since this is, by construction, an inequality. | 460,340 |
def interior_contains(self, Vobj): """ Tests whether the interior of the halfspace (excluding its boundary) defined by the inequality contains the given vertex/ray/line. | def interior_contains(self, Vobj): If you pass a vector, it is assumed to be the coordinate vector of a point:: sage: P = Polyhedron(vertices=[[1,1],[1,-1],[-1,1],[-1,-1]]) sage: p = vector(ZZ, [1,0] ) sage: [ ieq.interior_contains(p) for ieq in P.inequality_generator() ] [True, True, True, False] """ try: if Vobj.is... | 460,341 |
def is_equation(self): """ Tests if this object is an equation. By construction, it must be. | def is_equation(self): """ Tests if this object is an equation. By construction, it must be. | 460,342 |
def is_vertex(self): """ Tests if this object is a vertex. By construction it always is. | def is_vertex(self): """ Tests if this object is a vertex. By construction it always is. | 460,343 |
def is_ray(self): """ Tests if this object is a ray. Always True by construction. | def is_ray(self): """ Tests if this object is a ray. Always True by construction. | 460,344 |
def is_line(self): """ Tests if the object is a line. By construction it must be. | def is_line(self): """ Tests if the object is a line. By construction it must be. | 460,345 |
def identity(self): """ Returns the identity projection. | def identity(self): """ Returns the identity projection. | 460,346 |
def identity(self): """ Returns the identity projection. | def identity(self): """ Returns the identity projection. | 460,347 |
def diamond_bracket_operator(self, d): r""" Return the diamond bracket d operator on this modular symbols space. | def diamond_bracket_operator(self, d): r""" Return the diamond bracket d operator on this modular symbols space. | 460,348 |
def matching_polynomial(self, complement=True, name=None): """ Computes the matching polynomial of the graph G. The algorithm used is a recursive one, based on the following observation: - If e is an edge of G, G' is the result of deleting the edge e, and G'' is the result of deleting each vertex in e, then the match... | def matching_polynomial(self, complement=True, name=None): """ Computes the matching polynomial of the graph G. The algorithm used is a recursive one, based on the following observation: - If e is an edge of G, G' is the result of deleting the edge e, and G'' is the result of deleting each vertex in e, then the match... | 460,349 |
def matching_polynomial(self, complement=True, name=None): """ Computes the matching polynomial of the graph G. The algorithm used is a recursive one, based on the following observation: - If e is an edge of G, G' is the result of deleting the edge e, and G'' is the result of deleting each vertex in e, then the match... | def matching_polynomial(self, complement=True, name=None): """ Computes the matching polynomial of the graph G. The algorithm used is a recursive one, based on the following observation: - If e is an edge of G, G' is the result of deleting the edge e, and G'' is the result of deleting each vertex in e, then the match... | 460,350 |
def matching_polynomial(self, complement=True, name=None): """ Computes the matching polynomial of the graph G. The algorithm used is a recursive one, based on the following observation: - If e is an edge of G, G' is the result of deleting the edge e, and G'' is the result of deleting each vertex in e, then the match... | def matching_polynomial(self, complement=True, name=None): """ Computes the matching polynomial of the graph G. The algorithm used is a recursive one, based on the following observation: - If e is an edge of G, G' is the result of deleting the edge e, and G'' is the result of deleting each vertex in e, then the match... | 460,351 |
def search_doc(string, extra1='', extra2='', extra3='', extra4='', extra5='', **kwds): """ Search Sage HTML documentation for lines containing ``string``. The search is case-sensitive. The file paths in the output are relative to ``$SAGE_ROOT/devel/sage/doc/output``. INPUT: same as for :func:`search_src`. OUTPUT: sa... | def search_doc(string, extra1='', extra2='', extra3='', extra4='', extra5='', **kwds): """ Search Sage HTML documentation for lines containing ``string``. The search is case-sensitive. The file paths in the output are relative to ``$SAGE_ROOT/devel/sage/doc/output``. INPUT: same as for :func:`search_src`. OUTPUT: sa... | 460,352 |
def tau_to_bitrade(t1, t2, t3): """ Given permutations t1, t2, t3 that represent a latin bitrade, convert them to an explicit latin bitrade (T1, T2). The result is unique up to isotopism. EXAMPLE:: sage: from sage.combinat.matrices.latin import * sage: T1 = back_circulant(5) sage: x = isotopism( (0,1,2,3,4) ) sage: y... | def tau_to_bitrade(t1, t2, t3): """ Given permutations t1, t2, t3 that represent a latin bitrade, convert them to an explicit latin bitrade (T1, T2). The result is unique up to isotopism. EXAMPLE:: sage: from sage.combinat.matrices.latin import * sage: T1 = back_circulant(5) sage: x = isotopism( (0,1,2,3,4) ) sage: y... | 460,353 |
def is_row_and_col_balanced(T1, T2): """ Partial latin squares T1 and T2 are balanced if the symbols appearing in row r of T1 are the same as the symbols appearing in row r of T2, for each r, and if the same condition holds on columns. EXAMPLES:: sage: from sage.combinat.matrices.latin import * sage: T1 = matrix([[0,... | def is_row_and_col_balanced(T1, T2): """ Partial latin squares T1 and T2 are balanced if the symbols appearing in row r of T1 are the same as the symbols appearing in row r of T2, for each r, and if the same condition holds on columns. EXAMPLES:: sage: from sage.combinat.matrices.latin import * sage: T1 = matrix([[0,... | 460,354 |
def is_row_and_col_balanced(T1, T2): """ Partial latin squares T1 and T2 are balanced if the symbols appearing in row r of T1 are the same as the symbols appearing in row r of T2, for each r, and if the same condition holds on columns. EXAMPLES:: sage: from sage.combinat.matrices.latin import * sage: T1 = matrix([[0,... | def is_row_and_col_balanced(T1, T2): """ Partial latin squares T1 and T2 are balanced if the symbols appearing in row r of T1 are the same as the symbols appearing in row r of T2, for each r, and if the same condition holds on columns. EXAMPLES:: sage: from sage.combinat.matrices.latin import * sage: T1 = matrix([[0,... | 460,355 |
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. | 460,356 |
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. | 460,357 |
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. | 460,358 |
def coerce_field(self, other): """ Return the number type that contains both `self.field()` and `other`. | def coerce_field(self, other): """ Return the number type that contains both `self.field()` and `other`. | 460,359 |
def coerce_field(self, other): """ Return the number type that contains both `self.field()` and `other`. | def coerce_field(self, other): """ Return the number type that contains both `self.field()` and `other`. | 460,360 |
def coerce_field(self, other): """ Return the number type that contains both `self.field()` and `other`. | def coerce_field(self, other): """ Return the number type that contains both `self.field()` and `other`. | 460,361 |
def coerce_field(self, other): """ Return the number type that contains both `self.field()` and `other`. | def coerce_field(self, other): """ Return the number type that contains both `self.field()` and `other`. | 460,362 |
def coerce_field(self, other): """ Return the number type that contains both `self.field()` and `other`. | def coerce_field(self, other): """ Return the number type that contains both `self.field()` and `other`. | 460,363 |
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. | 460,364 |
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. | 460,365 |
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. | 460,366 |
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. | 460,367 |
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. | 460,368 |
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. | 460,369 |
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. | 460,370 |
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. | 460,371 |
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. | 460,372 |
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. | 460,373 |
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. | 460,374 |
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. | 460,375 |
def local_coordinates_at_nonweierstrass(self, P, prec = 20, name = 't'): """ For a non-Weierstrass point P = (a,b) on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x - a is the local parameter. | def local_coordinates_at_nonweierstrass(self, P, prec = 20, name = 't'): """ For a non-Weierstrass point P = (a,b) on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x - a is the local parameter. | 460,376 |
def local_coordinates_at_nonweierstrass(self, P, prec = 20, name = 't'): """ For a non-Weierstrass point P = (a,b) on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x - a is the local parameter. | deflocal_coordinates_at_nonweierstrass(self,P,prec=20,name='t'):"""Foranon-WeierstrasspointP=(a,b)onthehyperellipticcurvey^2=f(x),returns(x(t),y(t))suchthat(y(t))^2=f(x(t)),wheret=x-aisthelocalparameter. | 460,377 |
def local_coordinates_at_nonweierstrass(self, P, prec = 20, name = 't'): """ For a non-Weierstrass point P = (a,b) on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x - a is the local parameter. | def local_coordinates_at_nonweierstrass(self, P, prec = 20, name = 't'): """ For a non-Weierstrass point P = (a,b) on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x - a is the local parameter. | 460,378 |
def local_coordinates_at_nonweierstrass(self, P, prec = 20, name = 't'): """ For a non-Weierstrass point P = (a,b) on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x - a is the local parameter. | def local_coordinates_at_nonweierstrass(self, P, prec = 20, name = 't'): """ For a non-Weierstrass point P = (a,b) on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x - a is the local parameter. | 460,379 |
def local_coordinates_at_nonweierstrass(self, P, prec = 20, name = 't'): """ For a non-Weierstrass point P = (a,b) on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x - a is the local parameter. | def local_coordinates_at_nonweierstrass(self, P, prec = 20, name = 't'): """ For a non-Weierstrass point P = (a,b) on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x - a is the local parameter. | 460,380 |
def local_coordinates_at_weierstrass(self, P, prec = 20, name = 't'): """ For a finite Weierstrass point on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = y is the local parameter. | def local_coordinates_at_weierstrass(self, P, prec = 20, name = 't'): """ For a finite Weierstrass point on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = y is the local parameter. | 460,381 |
def local_coordinates_at_weierstrass(self, P, prec = 20, name = 't'): """ For a finite Weierstrass point on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = y is the local parameter. | def local_coordinates_at_weierstrass(self, P, prec = 20, name = 't'): """ For a finite Weierstrass point on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = y is the local parameter. | 460,382 |
def local_coordinates_at_weierstrass(self, P, prec = 20, name = 't'): """ For a finite Weierstrass point on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = y is the local parameter. | def local_coordinates_at_weierstrass(self, P, prec = 20, name = 't'): """ For a finite Weierstrass point on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = y is the local parameter. | 460,383 |
def local_coordinates_at_infinity(self, prec = 20, name = 't'): """ For the genus g hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x^g/y is the local parameter at infinity | deflocal_coordinates_at_infinity(self,prec=20,name='t'):"""Forthegenusghyperellipticcurvey^2=f(x),returns(x(t),y(t))suchthat(y(t))^2=f(x(t)),wheret=x^g/yisthelocalparameteratinfinity | 460,384 |
def local_coordinates_at_infinity(self, prec = 20, name = 't'): """ For the genus g hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x^g/y is the local parameter at infinity | deflocal_coordinates_at_infinity(self,prec=20,name='t'):"""Forthegenusghyperellipticcurvey^2=f(x),returns(x(t),y(t))suchthat(y(t))^2=f(x(t)),wheret=x^g/yisthelocalparameteratinfinity | 460,385 |
def local_coordinates_at_infinity(self, prec = 20, name = 't'): """ For the genus g hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x^g/y is the local parameter at infinity | def local_coordinates_at_infinity(self, prec = 20, name = 't'): """ For the genus g hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x^g/y is the local parameter at infinity | 460,386 |
def local_coord(self, P, prec = 20, name = 't'): """ If P is not infinity, calls the appropriate local_coordinates function. | def local_coord(self, P, prec = 20, name = 't'): """ If P is not infinity, calls the appropriate local_coordinates function. | 460,387 |
def local_coord(self, P, prec = 20, name = 't'): """ If P is not infinity, calls the appropriate local_coordinates function. | def local_coord(self, P, prec = 20, name = 't'): """ If P is not infinity, calls the appropriate local_coordinates function. | 460,388 |
def sturm_bound(self, M=None): r""" For a space M of modular forms, this function returns an integer B such that two modular forms in either self or M are equal if and only if their q-expansions are equal to precision B (note that this is 1+ the usual Sturm bound, since `O(q^\mathrm{prec})` has precision prec). If M is... | def sturm_bound(self, M=None): r""" For a space M of modular forms, this function returns an integer B such that two modular forms in either self or M are equal if and only if their q-expansions are equal to precision B (note that this is 1+ the usual Sturm bound, since `O(q^\mathrm{prec})` has precision prec). If M is... | 460,389 |
def sturm_bound(self, M=None): r""" For a space M of modular forms, this function returns an integer B such that two modular forms in either self or M are equal if and only if their q-expansions are equal to precision B (note that this is 1+ the usual Sturm bound, since `O(q^\mathrm{prec})` has precision prec). If M is... | def sturm_bound(self, M=None): r""" For a space M of modular forms, this function returns an integer B such that two modular forms in either self or M are equal if and only if their q-expansions are equal to precision B (note that this is 1+ the usual Sturm bound, since `O(q^\mathrm{prec})` has precision prec). If M is... | 460,390 |
def sturm_bound(self, M=None): r""" For a space M of modular forms, this function returns an integer B such that two modular forms in either self or M are equal if and only if their q-expansions are equal to precision B (note that this is 1+ the usual Sturm bound, since `O(q^\mathrm{prec})` has precision prec). If M is... | def sturm_bound(self, M=None): r""" For a space M of modular forms, this function returns an integer B such that two modular forms in either self or M are equal if and only if their q-expansions are equal to precision B (note that this is 1+ the usual Sturm bound, since `O(q^\mathrm{prec})` has precision prec). If M is... | 460,391 |
def NumberField(polynomial, name=None, check=True, names=None, cache=True, embedding=None, latex_name=None): r""" Return *the* number field defined by the given irreducible polynomial and with variable with the given name. If check is True (the default), also verify that the defining polynomial is irreducible and over ... | def NumberField(polynomial, name=None, check=True, names=None, cache=True, embedding=None, latex_name=None): r""" Return *the* number field defined by the given irreducible polynomial and with variable with the given name. If check is True (the default), also verify that the defining polynomial is irreducible and over ... | 460,392 |
def QuadraticField(D, names, check=True, embedding=True, latex_name=None): r""" Return a quadratic field obtained by adjoining a square root of `D` to the rational numbers, where `D` is not a perfect square. INPUT: - ``D`` - a rational number - ``names`` - variable name - ``check`` - bool (default: True) - ``... | def QuadraticField(D, names, check=True, embedding=True, latex_name='sqrt'): r""" Return a quadratic field obtained by adjoining a square root of `D` to the rational numbers, where `D` is not a perfect square. INPUT: - ``D`` - a rational number - ``names`` - variable name - ``check`` - bool (default: True) - ... | 460,393 |
def QuadraticField(D, names, check=True, embedding=True, latex_name=None): r""" Return a quadratic field obtained by adjoining a square root of `D` to the rational numbers, where `D` is not a perfect square. INPUT: - ``D`` - a rational number - ``names`` - variable name - ``check`` - bool (default: True) - ``... | def QuadraticField(D, names, check=True, embedding=True, latex_name=None): r""" Return a quadratic field obtained by adjoining a square root of `D` to the rational numbers, where `D` is not a perfect square. INPUT: - ``D`` - a rational number - ``names`` - variable name - ``check`` - bool (default: True) - ``... | 460,394 |
def QuadraticField(D, names, check=True, embedding=True, latex_name=None): r""" Return a quadratic field obtained by adjoining a square root of `D` to the rational numbers, where `D` is not a perfect square. INPUT: - ``D`` - a rational number - ``names`` - variable name - ``check`` - bool (default: True) - ``... | def QuadraticField(D, names, check=True, embedding=True, latex_name=None): r""" Return a quadratic field obtained by adjoining a square root of `D` to the rational numbers, where `D` is not a perfect square. INPUT: - ``D`` - a rational number - ``names`` - variable name - ``check`` - bool (default: True) - ``... | 460,395 |
def _sage_(self, R=None): """ Coerces self to Sage. EXAMPLES:: sage: R = singular.ring(0, '(x,y,z)', 'dp') sage: A = singular.matrix(2,2) sage: A._sage_(ZZ) [0 0] [0 0] sage: A = random_matrix(ZZ,3,3); A [ -8 2 1] [ -1 2 1] [-95 -1 -2] sage: As = singular(A); As -8 2 1 -1 2 1 -95 -1 -2... | def _sage_(self, R=None): """ Coerces self to Sage. EXAMPLES:: sage: R = singular.ring(0, '(x,y,z)', 'dp') sage: A = singular.matrix(2,2) sage: A._sage_(ZZ) [0 0] [0 0] sage: A = random_matrix(ZZ,3,3); A [ -8 2 1] [ -1 2 1] [-95 -1 -2] sage: As = singular(A); As -8 2 1 -1 2 1 -95 -1 -2 ... | 460,396 |
def bin_to_ascii(B): r""" Return the ASCII representation of the binary string ``B``. INPUT: - ``B`` -- a non-empty binary string or a non-empty list of bits. The number of bits in ``B`` must be a multiple of 8. OUTPUT: - The ASCII string corresponding to ``B``. ALGORITHM: Consider a block of bits `B = b_0 b_1 \c... | def bin_to_ascii(B): r""" Return the ASCII representation of the binary string ``B``. INPUT: - ``B`` -- a non-empty binary string or a non-empty list of bits. The number of bits in ``B`` must be a multiple of 8. OUTPUT: - The ASCII string corresponding to ``B``. ALGORITHM: Consider a block of bits `B = b_0 b_1 \c... | 460,397 |
sage: def my_carmichael(n): | sage: def my_carmichael(n): | 460,398 |
sage: def my_carmichael(n): | sage: def my_carmichael(n): | 460,399 |
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