bugged stringlengths 4 228k | fixed stringlengths 0 96.3M | __index_level_0__ int64 0 481k |
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def view(objects, title='SAGE', debug=False, sep='', tiny=False, pdflatex=None, viewer = None, tightpage = None, mode='inline', **kwds): r"""nodetex Compute a latex representation of each object in objects, compile, and display typeset. If used from the command line, this requires that latex be installed. INPUT: - `... | def view(objects, title='SAGE', debug=False, sep='', tiny=False, pdflatex=None, viewer = None, tightpage = None, mode='inline', **kwds): r"""nodetex Compute a latex representation of each object in objects, compile, and display typeset. If used from the command line, this requires that latex be installed. INPUT: - `... | 461,500 |
def view(objects, title='SAGE', debug=False, sep='', tiny=False, pdflatex=None, viewer = None, tightpage = None, mode='inline', **kwds): r"""nodetex Compute a latex representation of each object in objects, compile, and display typeset. If used from the command line, this requires that latex be installed. INPUT: - `... | def view(objects, title='SAGE', debug=False, sep='', tiny=False, pdflatex=None, viewer = None, tightpage = None, mode='inline', **kwds): r"""nodetex Compute a latex representation of each object in objects, compile, and display typeset. If used from the command line, this requires that latex be installed. INPUT: - `... | 461,501 |
def view(objects, title='SAGE', debug=False, sep='', tiny=False, pdflatex=None, viewer = None, tightpage = None, mode='inline', **kwds): r"""nodetex Compute a latex representation of each object in objects, compile, and display typeset. If used from the command line, this requires that latex be installed. INPUT: - `... | defview(objects,title='SAGE',debug=False,sep='',tiny=False,pdflatex=None,viewer=None,tightpage=None,mode='inline',**kwds):r"""nodetexComputealatexrepresentationofeachobjectinobjects,compile,anddisplaytypeset.Ifusedfromthecommandline,thisrequiresthatlatexbeinstalled.INPUT:-``objects``-list(orobject)-``title``-string(def... | 461,502 |
def png(x, filename, density=150, debug=False, do_in_background=False, tiny=False, pdflatex=True): """ Create a png image representation of ``x`` and save to the given filename. INPUT: - ``x`` - object to be displayed - ``filename`` - file in which to save the image - ``density`` - integer (default: 150) - ``d... | def png(x, filename, density=150, debug=False, do_in_background=False, tiny=False, pdflatex=True, engine='pdflatex'): """ Create a png image representation of ``x`` and save to the given filename. INPUT: - ``x`` - object to be displayed - ``filename`` - file in which to save the image - ``density`` - integer (de... | 461,503 |
def png(x, filename, density=150, debug=False, do_in_background=False, tiny=False, pdflatex=True): """ Create a png image representation of ``x`` and save to the given filename. INPUT: - ``x`` - object to be displayed - ``filename`` - file in which to save the image - ``density`` - integer (default: 150) - ``d... | def png(x, filename, density=150, debug=False, do_in_background=False, tiny=False, pdflatex=True): """ Create a png image representation of ``x`` and save to the given filename. INPUT: - ``x`` - object to be displayed - ``filename`` - file in which to save the image - ``density`` - integer (default: 150) - ``d... | 461,504 |
def png(x, filename, density=150, debug=False, do_in_background=False, tiny=False, pdflatex=True): """ Create a png image representation of ``x`` and save to the given filename. INPUT: - ``x`` - object to be displayed - ``filename`` - file in which to save the image - ``density`` - integer (default: 150) - ``d... | def png(x, filename, density=150, debug=False, do_in_background=False, tiny=False, pdflatex=True): """ Create a png image representation of ``x`` and save to the given filename. INPUT: - ``x`` - object to be displayed - ``filename`` - file in which to save the image - ``density`` - integer (default: 150) - ``d... | 461,505 |
def repr_lincomb(symbols, coeffs): r""" Compute a latex representation of a linear combination of some formal symbols. INPUT: - ``symbols`` - list of symbols - ``coeffs`` - list of coefficients of the symbols OUTPUT: a string EXAMPLES:: sage: t = PolynomialRing(QQ, 't').0 sage: from sage.misc.latex import repr_... | defrepr_lincomb(symbols,coeffs):r"""Computealatexrepresentationofalinearcombinationofsomeformalsymbols.INPUT:-``symbols``-listofsymbols-``coeffs``-listofcoefficientsofthesymbolsOUTPUT:astringEXAMPLES::sage:t=PolynomialRing(QQ,'t').0sage:fromsage.misc.lateximportrepr_lincombsage:repr_lincomb(['a','s',''],[-t,t-2,t^12+2]... | 461,506 |
def print_or_typeset(object): r""" 'view' or 'print' the object depending on the situation. In particular, if in notebook mode with the typeset box checked, view the object. Otherwise, print the object. INPUT: object: anything EXAMPLES:: sage: sage.misc.latex.print_or_typeset(3) 3 sage: sage.misc.latex.EMBEDDED_MOD... | defprint_or_typeset(object):r"""'view'or'print'theobjectdependingonthesituation.Inparticular,ifinnotebookmodewiththetypesetboxchecked,viewtheobject.Otherwise,printtheobject.INPUT:object:anythingEXAMPLES::sage:sage.misc.latex.print_or_typeset(3)3sage:sage.misc.latex.EMBEDDED_MODE=Truesage:sage.misc.latex.print_or_typese... | 461,507 |
def pretty_print (object): r""" Try to pretty print an object in an intelligent way. For graphics objects, this returns their default representation. For other objects, in the notebook, this calls the :func:`view` command, while from the command line, this produces an html string suitable for processing by jsMath. I... | defpretty_print(object):r"""Trytoprettyprintanobjectinanintelligentway.Forgraphicsobjects,thisreturnstheirdefaultrepresentation.Forotherobjects,inthenotebook,thiscallsthe:func:`view`command,whilefromthecommandline,thisproducesanhtmlstringsuitableforprocessingbyjsMath.INPUT:-``object``-aSageobjectThisfunctionisusedinthe... | 461,508 |
def pretty_print_default(enable=True): r""" Enable or disable default pretty printing. Pretty printing means rendering things so that jsMath or some other latex-aware front end can render real math. INPUT: - ``enable`` - bool (optional, default True). If True, turn on pretty printing; if False, turn it off. EXAMPL... | defpretty_print_default(enable=True):r"""Enableordisabledefaultprettyprinting.PrettyprintingmeansrenderingthingssothatjsMathorsomeotherlatex-awarefrontendcanrenderrealmath.INPUT:-``enable``-bool(optional,defaultTrue).IfTrue,turnonprettyprinting;ifFalse,turnitoff.EXAMPLES::sage:pretty_print_default(True)sage:sys.display... | 461,509 |
def coleman_integrals_on_basis(self, P, Q, algorithm=None): """ | def coleman_integrals_on_basis(self, P, Q, algorithm=None): """ | 461,510 |
def coleman_integrals_on_basis(self, P, Q, algorithm=None): """ | def coleman_integrals_on_basis(self, P, Q, algorithm=None): """ | 461,511 |
def coleman_integrals_on_basis(self, P, Q, algorithm=None): """ | def coleman_integrals_on_basis(self, P, Q, algorithm=None): """ | 461,512 |
def coleman_integrals_on_basis(self, P, Q, algorithm=None): """ | def coleman_integrals_on_basis(self, P, Q, algorithm=None): """ | 461,513 |
def coleman_integrals_on_basis(self, P, Q, algorithm=None): """ | def coleman_integrals_on_basis(self, P, Q, algorithm=None): """ | 461,514 |
def coleman_integrals_on_basis(self, P, Q, algorithm=None): """ | defcoleman_integrals_on_basis(self,P,Q,algorithm=None):""" | 461,515 |
def coleman_integrals_on_basis(self, P, Q, algorithm=None): """ | defcoleman_integrals_on_basis(self,P,Q,algorithm=None):""" | 461,516 |
def coleman_integrals_on_basis(self, P, Q, algorithm=None): """ | defcoleman_integrals_on_basis(self,P,Q,algorithm=None):""" | 461,517 |
def coleman_integrals_on_basis(self, P, Q, algorithm=None): """ | def coleman_integrals_on_basis(self, P, Q, algorithm=None): """ | 461,518 |
def coleman_integrals_on_basis(self, P, Q, algorithm=None): """ | defcoleman_integrals_on_basis(self,P,Q,algorithm=None):""" | 461,519 |
def coleman_integrals_on_basis(self, P, Q, algorithm=None): """ | defcoleman_integrals_on_basis(self,P,Q,algorithm=None):""" | 461,520 |
def coleman_integral(self, w, P, Q, algorithm = 'None'): """ INPUT: - w differential (if one of P,Q is Weierstrass, w must be odd) - P point on self - Q point on self - algorithm (optional) = None (uses Frobenius) or teichmuller (uses Teichmuller points) | def coleman_integral(self, w, P, Q, algorithm = 'None'): """ INPUT: - w differential (if one of P,Q is Weierstrass, w must be odd) - P point on self - Q point on self - algorithm (optional) = None (uses Frobenius) or teichmuller (uses Teichmuller points) | 461,521 |
def coleman_integral(self, w, P, Q, algorithm = 'None'): """ INPUT: - w differential (if one of P,Q is Weierstrass, w must be odd) - P point on self - Q point on self - algorithm (optional) = None (uses Frobenius) or teichmuller (uses Teichmuller points) | def coleman_integral(self, w, P, Q, algorithm = 'None'): """ INPUT: - w differential (if one of P,Q is Weierstrass, w must be odd) - P point on self - Q point on self - algorithm (optional) = None (uses Frobenius) or teichmuller (uses Teichmuller points) | 461,522 |
def coleman_integral(self, w, P, Q, algorithm = 'None'): """ INPUT: - w differential (if one of P,Q is Weierstrass, w must be odd) - P point on self - Q point on self - algorithm (optional) = None (uses Frobenius) or teichmuller (uses Teichmuller points) | def coleman_integral(self, w, P, Q, algorithm = 'None'): """ INPUT: - w differential (if one of P,Q is Weierstrass, w must be odd) - P point on self - Q point on self - algorithm (optional) = None (uses Frobenius) or teichmuller (uses Teichmuller points) | 461,523 |
def coleman_integral(self, w, P, Q, algorithm = 'None'): """ INPUT: - w differential (if one of P,Q is Weierstrass, w must be odd) - P point on self - Q point on self - algorithm (optional) = None (uses Frobenius) or teichmuller (uses Teichmuller points) | def coleman_integral(self, w, P, Q, algorithm = 'None'): """ INPUT: - w differential (if one of P,Q is Weierstrass, w must be odd) - P point on self - Q point on self - algorithm (optional) = None (uses Frobenius) or teichmuller (uses Teichmuller points) | 461,524 |
def curve_over_ram_extn(self,deg): """ self over Qp(p^(1/deg)) INPUT: - deg: the degree of the ramified extension OUTPUT: self over Qp(p^(1/deg)) | def curve_over_ram_extn(self,deg): """ self over Qp(p^(1/deg)) INPUT: - deg: the degree of the ramified extension OUTPUT: self over Qp(p^(1/deg)) | 461,525 |
def derivative(self, ex, operator): """ EXAMPLES:: | def derivative(self, ex, operator): """ EXAMPLES:: | 461,526 |
def derivative(self, ex, operator): """ EXAMPLES:: | def derivative(self, ex, operator): """ EXAMPLES:: | 461,527 |
def derivative(self, ex, operator): """ EXAMPLES:: | def derivative(self, ex, operator): """ EXAMPLES:: | 461,528 |
def derivative(self, ex, operator): """ EXAMPLES:: | def derivative(self, ex, operator): """ EXAMPLES:: | 461,529 |
def __mul__(self, other): r""" Calculate the product self * other. | def __mul__(self, other): r""" Calculate the product self * other. | 461,530 |
def metaclass(name, bases): """ Creates a new class in this metaclass INPUT:: - name: a string - bases: a tuple of classes EXAMPLES:: sage: from sage.misc.test_class_pickling import metaclass, bar sage: c = metaclass("foo2", (object, bar,)) constructing class sage: c <class 'sage.misc.test_class_pickling.foo2'> sage... | def metaclass(name, bases): """ Creates a new class in this metaclass INPUT:: - name: a string - bases: a tuple of classes EXAMPLES:: sage: from sage.misc.test_class_pickling import metaclass, bar sage: c = metaclass("foo2", (object, bar,)) constructing class sage: c <class 'sage.misc.test_class_pickling.foo2'> sage... | 461,531 |
def identity_matrix(ring, n=0, sparse=False): r""" Return the `n \times n` identity matrix over the given ring. The default ring is the integers. EXAMPLES:: sage: M = identity_matrix(QQ, 2); M [1 0] [0 1] sage: M.parent() Full MatrixSpace of 2 by 2 dense matrices over Rational Field sage: M = identity_matrix(2); M [... | def identity_matrix(ring, n=0, sparse=False): r""" Return the `n \times n` identity matrix over the given ring. The default ring is the integers. EXAMPLES:: sage: M = identity_matrix(QQ, 2); M [1 0] [0 1] sage: M.parent() Full MatrixSpace of 2 by 2 dense matrices over Rational Field sage: M = identity_matrix(2); M [... | 461,532 |
def zero_matrix(ring, nrows, ncols=None, sparse=False): r""" Return the `nrows \times ncols` zero matrix over the given ring. The default ring is the integers. EXAMPLES:: sage: M = zero_matrix(QQ, 2); M [0 0] [0 0] sage: M.parent() Full MatrixSpace of 2 by 2 dense matrices over Rational Field sage: M = zero_matrix(2... | def zero_matrix(ring, nrows, ncols=None, sparse=False): r""" Return the `nrows \times ncols` zero matrix over the given ring. The default ring is the integers. EXAMPLES:: sage: M = zero_matrix(QQ, 2); M [0 0] [0 0] sage: M.parent() Full MatrixSpace of 2 by 2 dense matrices over Rational Field sage: M = zero_matrix(2... | 461,533 |
def __call__(self, w, order=1, datatype='iter'): r""" Returns the image of ``w`` under self to the given order. INPUT: | def __call__(self, w, order=1, datatype='iter'): r""" Returns the image of ``w`` under self to the given order. INPUT: | 461,534 |
def __call__(self, w, order=1, datatype='iter'): r""" Returns the image of ``w`` under self to the given order. INPUT: | def __call__(self, w, order=1, datatype='iter'): r""" Returns the image of ``w`` under self to the given order. INPUT: | 461,535 |
def __call__(self, w, order=1, datatype='iter'): r""" Returns the image of ``w`` under self to the given order. INPUT: | def __call__(self, w, order=1, datatype='iter'): r""" Returns the image of ``w`` under self to the given order. INPUT: | 461,536 |
def is_prolongable(self, letter): r""" Returns ``True`` if ``self`` is prolongable on ``letter``. A morphism `\varphi` is prolongable on a letter `a` if `a` is a prefix of `\varphi(a)`. INPUT: | def is_prolongable(self, letter): r""" Returns ``True`` if ``self`` is prolongable on ``letter``. A morphism `\varphi` is prolongable on a letter `a` if `a` is a prefix of `\varphi(a)`. INPUT: | 461,537 |
def is_prolongable(self, letter): r""" Returns ``True`` if ``self`` is prolongable on ``letter``. A morphism `\varphi` is prolongable on a letter `a` if `a` is a prefix of `\varphi(a)`. INPUT: | defis_prolongable(self,letter):r"""Returns``True``if``self``isprolongableon``letter``.Amorphism`\varphi`isprolongableonaletter`a`if`a`isaprefixof`\varphi(a)`.INPUT: | 461,538 |
def is_prolongable(self, letter): r""" Returns ``True`` if ``self`` is prolongable on ``letter``. A morphism `\varphi` is prolongable on a letter `a` if `a` is a prefix of `\varphi(a)`. INPUT: | def is_prolongable(self, letter): r""" Returns ``True`` if ``self`` is prolongable on ``letter``. A morphism `\varphi` is prolongable on a letter `a` if `a` is a prefix of `\varphi(a)`. INPUT: | 461,539 |
def letter_iterator(self, letter): r""" Returns an iterator of the letters of the fixed point of ``self`` starting with ``letter``. | def _fixed_point_iterator(self, letter): r""" Returns an iterator of the letters of the fixed point of ``self`` starting with ``letter``. | 461,540 |
def letter_iterator(self, letter): r""" Returns an iterator of the letters of the fixed point of ``self`` starting with ``letter``. | def letter_iterator(self, letter): r""" Returns an iterator of the letters of the fixed point of ``self`` starting with ``letter``. | 461,541 |
def letter_iterator(self, letter): r""" Returns an iterator of the letters of the fixed point of ``self`` starting with ``letter``. | def letter_iterator(self, letter): r""" Returns an iterator of the letters of the fixed point of ``self`` starting with ``letter``. | 461,542 |
def letter_iterator(self, letter): r""" Returns an iterator of the letters of the fixed point of ``self`` starting with ``letter``. | def letter_iterator(self, letter): r""" Returns an iterator of the letters of the fixed point of ``self`` starting with ``letter``. | 461,543 |
def letter_iterator(self, letter): r""" Returns an iterator of the letters of the fixed point of ``self`` starting with ``letter``. | def letter_iterator(self, letter): r""" Returns an iterator of the letters of the fixed point of ``self`` starting with ``letter``. | 461,544 |
def fixed_point(self, letter): r""" Returns the fixed point of ``self`` beginning by the given ``letter``. | def fixed_point(self, letter): r""" Returns the fixed point of ``self`` beginning by the given ``letter``. | 461,545 |
def fixed_point(self, letter): r""" Returns the fixed point of ``self`` beginning by the given ``letter``. | def fixed_point(self, letter): r""" Returns the fixed point of ``self`` beginning by the given ``letter``. | 461,546 |
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... | 461,547 |
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. | 461,548 |
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... | 461,549 |
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. | 461,550 |
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. | 461,551 |
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. | 461,552 |
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. | 461,553 |
def identity(self): """ Returns the identity projection. | def identity(self): """ Returns the identity projection. | 461,554 |
def identity(self): """ Returns the identity projection. | def identity(self): """ Returns the identity projection. | 461,555 |
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. | 461,556 |
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. | 461,557 |
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. | 461,558 |
def _sage_doc_(self): """ EXAMPLES:: sage: 'groebner' in singular.groebner._sage_doc_() True """ if not nodes: generate_docstring_dictionary() | def _sage_doc_(self): """ EXAMPLES:: sage: 'groebner' in singular.groebner._sage_doc_() True """ if not nodes: generate_docstring_dictionary() | 461,559 |
def __call__(self, P): r""" Returns a rational point P in the abstract Homset J(K), given: 0. A point P in J = Jac(C), returning P; 1. A point P on the curve C such that J = Jac(C), where C is an odd degree model, returning [P - oo]; 2. A pair of points (P, Q) on the curve C such that J = Jac(C), returning [P-Q]; 2. A... | def __call__(self, P): r""" Returns a rational point P in the abstract Homset J(K), given: 0. A point P in J = Jac(C), returning P; 1. A point P on the curve C such that J = Jac(C), where C is an odd degree model, returning [P - oo]; 2. A pair of points (P, Q) on the curve C such that J = Jac(C), returning [P-Q]; 2. A... | 461,560 |
def is_square_free(self): r""" Returns True if self does not contain squares, and False otherwise. EXAMPLES:: sage: W = Words('123') sage: W('12312').is_square_free() True sage: W('31212').is_square_free() False sage: W().is_square_free() True """ l = self.length() if l < 2: return True suff = self for i in xrange(0,... | def is_square_free(self): r""" Returns True if self does not contain squares, and False otherwise. EXAMPLES:: sage: W = Words('123') sage: W('12312').is_square_free() True sage: W('31212').is_square_free() False sage: W().is_square_free() True """ l = self.length() if l < 2: return True suff = self for i in xrange(0,... | 461,561 |
def edges(self, labels=True, sort=True, key=None): r""" Return a list of the edges of the graph as triples (u,v,l) where u and v are vertices and l is a label. | def edges(self, labels=True, sort=True, key=None): r""" Return a list of the edges of the graph as triples (u,v,l) where u and v are vertices and l is a label. | 461,562 |
def edge_boundary(self, vertices1, vertices2=None, labels=True): """ Returns a list of edges `(u,v,l)` with `u` in ``vertices1`` and `v` in ``vertices2``. If ``vertices2`` is ``None``, then it is set to the complement of ``vertices1``. In a digraph, the external boundary of a vertex `v` are those vertices `u` with an ... | def edge_boundary(self, vertices1, vertices2=None, labels=True, sort=True): """ Returns a list of edges `(u,v,l)` with `u` in ``vertices1`` and `v` in ``vertices2``. If ``vertices2`` is ``None``, then it is set to the complement of ``vertices1``. In a digraph, the external boundary of a vertex `v` are those vertices `... | 461,563 |
def edge_boundary(self, vertices1, vertices2=None, labels=True): """ Returns a list of edges `(u,v,l)` with `u` in ``vertices1`` and `v` in ``vertices2``. If ``vertices2`` is ``None``, then it is set to the complement of ``vertices1``. In a digraph, the external boundary of a vertex `v` are those vertices `u` with an ... | def edge_boundary(self, vertices1, vertices2=None, labels=True): """ Returns a list of edges `(u,v,l)` with `u` in ``vertices1`` and `v` in ``vertices2``. If ``vertices2`` is ``None``, then it is set to the complement of ``vertices1``. In a digraph, the external boundary of a vertex `v` are those vertices `u` with an ... | 461,564 |
def edge_boundary(self, vertices1, vertices2=None, labels=True): """ Returns a list of edges `(u,v,l)` with `u` in ``vertices1`` and `v` in ``vertices2``. If ``vertices2`` is ``None``, then it is set to the complement of ``vertices1``. In a digraph, the external boundary of a vertex `v` are those vertices `u` with an ... | def edge_boundary(self, vertices1, vertices2=None, labels=True): """ Returns a list of edges `(u,v,l)` with `u` in ``vertices1`` and `v` in ``vertices2``. If ``vertices2`` is ``None``, then it is set to the complement of ``vertices1``. In a digraph, the external boundary of a vertex `v` are those vertices `u` with an ... | 461,565 |
def edge_boundary(self, vertices1, vertices2=None, labels=True): """ Returns a list of edges `(u,v,l)` with `u` in ``vertices1`` and `v` in ``vertices2``. If ``vertices2`` is ``None``, then it is set to the complement of ``vertices1``. In a digraph, the external boundary of a vertex `v` are those vertices `u` with an ... | def edge_boundary(self, vertices1, vertices2=None, labels=True): """ Returns a list of edges `(u,v,l)` with `u` in ``vertices1`` and `v` in ``vertices2``. If ``vertices2`` is ``None``, then it is set to the complement of ``vertices1``. In a digraph, the external boundary of a vertex `v` are those vertices `u` with an ... | 461,566 |
def edge_boundary(self, vertices1, vertices2=None, labels=True): """ Returns a list of edges `(u,v,l)` with `u` in ``vertices1`` and `v` in ``vertices2``. If ``vertices2`` is ``None``, then it is set to the complement of ``vertices1``. In a digraph, the external boundary of a vertex `v` are those vertices `u` with an ... | def edge_boundary(self, vertices1, vertices2=None, labels=True): """ Returns a list of edges `(u,v,l)` with `u` in ``vertices1`` and `v` in ``vertices2``. If ``vertices2`` is ``None``, then it is set to the complement of ``vertices1``. In a digraph, the external boundary of a vertex `v` are those vertices `u` with an ... | 461,567 |
def edge_boundary(self, vertices1, vertices2=None, labels=True): """ Returns a list of edges `(u,v,l)` with `u` in ``vertices1`` and `v` in ``vertices2``. If ``vertices2`` is ``None``, then it is set to the complement of ``vertices1``. In a digraph, the external boundary of a vertex `v` are those vertices `u` with an ... | def edge_boundary(self, vertices1, vertices2=None, labels=True): """ Returns a list of edges `(u,v,l)` with `u` in ``vertices1`` and `v` in ``vertices2``. If ``vertices2`` is ``None``, then it is set to the complement of ``vertices1``. In a digraph, the external boundary of a vertex `v` are those vertices `u` with an ... | 461,568 |
def edge_boundary(self, vertices1, vertices2=None, labels=True): """ Returns a list of edges `(u,v,l)` with `u` in ``vertices1`` and `v` in ``vertices2``. If ``vertices2`` is ``None``, then it is set to the complement of ``vertices1``. In a digraph, the external boundary of a vertex `v` are those vertices `u` with an ... | def edge_boundary(self, vertices1, vertices2=None, labels=True): """ Returns a list of edges `(u,v,l)` with `u` in ``vertices1`` and `v` in ``vertices2``. If ``vertices2`` is ``None``, then it is set to the complement of ``vertices1``. In a digraph, the external boundary of a vertex `v` are those vertices `u` with an ... | 461,569 |
def edge_boundary(self, vertices1, vertices2=None, labels=True): """ Returns a list of edges `(u,v,l)` with `u` in ``vertices1`` and `v` in ``vertices2``. If ``vertices2`` is ``None``, then it is set to the complement of ``vertices1``. In a digraph, the external boundary of a vertex `v` are those vertices `u` with an ... | def edge_boundary(self, vertices1, vertices2=None, labels=True): """ Returns a list of edges `(u,v,l)` with `u` in ``vertices1`` and `v` in ``vertices2``. If ``vertices2`` is ``None``, then it is set to the complement of ``vertices1``. In a digraph, the external boundary of a vertex `v` are those vertices `u` with an ... | 461,570 |
def edge_boundary(self, vertices1, vertices2=None, labels=True): """ Returns a list of edges `(u,v,l)` with `u` in ``vertices1`` and `v` in ``vertices2``. If ``vertices2`` is ``None``, then it is set to the complement of ``vertices1``. In a digraph, the external boundary of a vertex `v` are those vertices `u` with an ... | def edge_boundary(self, vertices1, vertices2=None, labels=True): """ Returns a list of edges `(u,v,l)` with `u` in ``vertices1`` and `v` in ``vertices2``. If ``vertices2`` is ``None``, then it is set to the complement of ``vertices1``. In a digraph, the external boundary of a vertex `v` are those vertices `u` with an ... | 461,571 |
def edge_iterator(self, vertices=None, labels=True, ignore_direction=False): """ Returns an iterator over the edges incident with any vertex given. If the graph is directed, iterates over edges going out only. If vertices is None, then returns an iterator over all edges. If self is directed, returns outgoing edges only... | def edge_iterator(self, vertices=None, labels=True, ignore_direction=False): """ Returns an iterator over edges. The iterator returned is over the edges incident with any vertex given in the parameter ``vertices``. If the graph is directed, iterates over edges going out only. If vertices is None, then returns an itera... | 461,572 |
def edge_iterator(self, vertices=None, labels=True, ignore_direction=False): """ Returns an iterator over the edges incident with any vertex given. If the graph is directed, iterates over edges going out only. If vertices is None, then returns an iterator over all edges. If self is directed, returns outgoing edges only... | def - ``vertices`` - (default: None) a vertex, a list of vertices or None edge_iterator(self, - ``vertices`` - (default: None) a vertex, a list of vertices or None vertices=None, - ``vertices`` - (default: None) a vertex, a list of vertices or None labels=True, - ``vertices`` - (default: None) a vertex, a list of verti... | 461,573 |
def edge_iterator(self, vertices=None, labels=True, ignore_direction=False): """ Returns an iterator over the edges incident with any vertex given. If the graph is directed, iterates over edges going out only. If vertices is None, then returns an iterator over all edges. If self is directed, returns outgoing edges only... | def edge_iterator(self, vertices=None, labels=True, ignore_direction=False): """ Returns an iterator over the edges incident with any vertex given. If the graph is directed, iterates over edges going out only. If vertices is None, then returns an iterator over all edges. If self is directed, returns outgoing edges only... | 461,574 |
def edge_iterator(self, vertices=None, labels=True, ignore_direction=False): """ Returns an iterator over the edges incident with any vertex given. If the graph is directed, iterates over edges going out only. If vertices is None, then returns an iterator over all edges. If self is directed, returns outgoing edges only... | def edge_iterator(self, vertices=None, labels=True, ignore_direction=False): """ Returns an iterator over the edges incident with any vertex given. If the graph is directed, iterates over edges going out only. If vertices is None, then returns an iterator over all edges. If self is directed, returns outgoing edges only... | 461,575 |
def edge_iterator(self, vertices=None, labels=True, ignore_direction=False): """ Returns an iterator over the edges incident with any vertex given. If the graph is directed, iterates over edges going out only. If vertices is None, then returns an iterator over all edges. If self is directed, returns outgoing edges only... | def edge_iterator(self, vertices=None, labels=True, ignore_direction=False): """ Returns an iterator over the edges incident with any vertex given. If the graph is directed, iterates over edges going out only. If vertices is None, then returns an iterator over all edges. If self is directed, returns outgoing edges only... | 461,576 |
def edge_iterator(self, vertices=None, labels=True, ignore_direction=False): """ Returns an iterator over the edges incident with any vertex given. If the graph is directed, iterates over edges going out only. If vertices is None, then returns an iterator over all edges. If self is directed, returns outgoing edges only... | def edge_iterator(self, vertices=None, labels=True, ignore_direction=False): """ Returns an iterator over the edges incident with any vertex given. If the graph is directed, iterates over edges going out only. If vertices is None, then returns an iterator over all edges. If self is directed, returns outgoing edges only... | 461,577 |
def edges_incident(self, vertices=None, labels=True): """ Returns a list of edges incident with any vertex given. If vertices is None, returns a list of all edges in graph. For digraphs, only lists outward edges. INPUT: - ``label`` - if False, each edge is a tuple (u,v) of vertices. EXAMPLES:: sage: graphs.Peter... | def edges_incident(self, vertices=None, labels=True): """ Returns a list of edges incident with any vertex given. If vertices is None, returns a list of all edges in graph. For digraphs, only lists outward edges. INPUT: - ``vertices`` - object (default: None) - a vertex, a list of vertices or None. - ``labels`` - b... | 461,578 |
def edges_incident(self, vertices=None, labels=True): """ Returns a list of edges incident with any vertex given. If vertices is None, returns a list of all edges in graph. For digraphs, only lists outward edges. INPUT: - ``label`` - if False, each edge is a tuple (u,v) of vertices. EXAMPLES:: sage: graphs.Peter... | def edges_incident(self, vertices=None, labels=True): """ Returns a list of edges incident with any vertex given. If vertices is None, returns a list of all edges in graph. For digraphs, only lists outward edges. INPUT: - ``label`` - if False, each edge is a tuple (u,v) of vertices. EXAMPLES:: sage: graphs.Peter... | 461,579 |
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. | 461,580 |
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. | 461,581 |
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. | 461,582 |
def set_precision(n): r""" Set the global NTL real number precision. This has a massive effect on the speed of mwrank calculations. The default (used if this function is not called) is n=15, but it might have to be increased if a computation fails. In this case, one must recreate the mwrank curve from scratch after ... | def set_precision(n): r""" Set the global NTL real number precision. This has a massive effect on the speed of mwrank calculations. The default (used if this function is not called) is ``n=15``, but it might have to be increased if a computation fails. In this case, one must recreate the mwrank curve from scratch af... | 461,583 |
def set_precision(n): r""" Set the global NTL real number precision. This has a massive effect on the speed of mwrank calculations. The default (used if this function is not called) is n=15, but it might have to be increased if a computation fails. In this case, one must recreate the mwrank curve from scratch after ... | def set_precision(n): r""" Set the global NTL real number precision. This has a massive effect on the speed of mwrank calculations. The default (used if this function is not called) is n=15, but it might have to be increased if a computation fails. In this case, one must recreate the mwrank curve from scratch after ... | 461,584 |
def set_precision(n): r""" Set the global NTL real number precision. This has a massive effect on the speed of mwrank calculations. The default (used if this function is not called) is n=15, but it might have to be increased if a computation fails. In this case, one must recreate the mwrank curve from scratch after ... | def set_precision(n): r""" Set the global NTL real number precision. This has a massive effect on the speed of mwrank calculations. The default (used if this function is not called) is n=15, but it might have to be increased if a computation fails. In this case, one must recreate the mwrank curve from scratch after ... | 461,585 |
def set_precision(n): r""" Set the global NTL real number precision. This has a massive effect on the speed of mwrank calculations. The default (used if this function is not called) is n=15, but it might have to be increased if a computation fails. In this case, one must recreate the mwrank curve from scratch after ... | def set_precision(n): r""" Set the global NTL real number precision. This has a massive effect on the speed of mwrank calculations. The default (used if this function is not called) is n=15, but it might have to be increased if a computation fails. In this case, one must recreate the mwrank curve from scratch after ... | 461,586 |
def __init__(self, ainvs, verbose=False): r""" Create the mwrank elliptic curve with invariants ``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. | def __init__(self, ainvs, verbose=False): r""" Create the mwrank elliptic curve with invariants ``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. | 461,587 |
def __init__(self, ainvs, verbose=False): r""" Create the mwrank elliptic curve with invariants ``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. | def __init__(self, ainvs, verbose=False): r""" Create the mwrank elliptic curve with invariants ``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. | 461,588 |
def __init__(self, ainvs, verbose=False): r""" Create the mwrank elliptic curve with invariants ``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. | def __init__(self, ainvs, verbose=False): r""" Create the mwrank elliptic curve with invariants ``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. | 461,589 |
def __init__(self, ainvs, verbose=False): r""" Create the mwrank elliptic curve with invariants ``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. | def __init__(self, ainvs, verbose=False): r""" Create the mwrank elliptic curve with invariants ``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. | 461,590 |
def __init__(self, ainvs, verbose=False): r""" Create the mwrank elliptic curve with invariants ``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. | def __init__(self, ainvs, verbose=False): r""" Create the mwrank elliptic curve with invariants ``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. | 461,591 |
def set_verbose(self, verbose): """ Set the verbosity of printing of output by the 2-descent and other functions. | def set_verbose(self, verbose): """ Set the verbosity of printing of output by the :meth:`two_descent()` and other functions. | 461,592 |
def set_verbose(self, verbose): """ Set the verbosity of printing of output by the 2-descent and other functions. | def set_verbose(self, verbose): """ Set the verbosity of printing of output by the 2-descent and other functions. | 461,593 |
def set_verbose(self, verbose): """ Set the verbosity of printing of output by the 2-descent and other functions. | def set_verbose(self, verbose): """ Set the verbosity of printing of output by the 2-descent and other functions. | 461,594 |
def _curve_data(self): r""" Returns the underlying _Curvedata class for this mwrank elliptic curve. | def _curve_data(self): r""" Returns the underlying _Curvedata class for this mwrank elliptic curve. | 461,595 |
def two_descent(self, verbose = True, selmer_only = False, first_limit = 20, second_limit = 8, n_aux = -1, second_descent = True): """ Compute 2-descent data for this curve. | def two_descent(self, verbose = True, selmer_only = False, first_limit = 20, second_limit = 8, n_aux = -1, second_descent = True): """ Compute 2-descent data for this curve. | 461,596 |
def two_descent(self, verbose = True, selmer_only = False, first_limit = 20, second_limit = 8, n_aux = -1, second_descent = True): """ Compute 2-descent data for this curve. | def two_descent(self, verbose = True, selmer_only = False, first_limit = 20, second_limit = 8, n_aux = -1, second_descent = True): """ Compute 2-descent data for this curve. | 461,597 |
def two_descent(self, verbose = True, selmer_only = False, first_limit = 20, second_limit = 8, n_aux = -1, second_descent = True): """ Compute 2-descent data for this curve. | def two_descent(self, verbose = True, selmer_only = False, first_limit = 20, second_limit = 8, n_aux = -1, second_descent = True): """ Compute 2-descent data for this curve. | 461,598 |
def two_descent(self, verbose = True, selmer_only = False, first_limit = 20, second_limit = 8, n_aux = -1, second_descent = True): """ Compute 2-descent data for this curve. | def two_descent(self, verbose = True, selmer_only = False, first_limit = 20, second_limit = 8, n_aux = -1, second_descent = True): """ Compute 2-descent data for this curve. | 461,599 |
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