bugged stringlengths 4 228k | fixed stringlengths 0 96.3M | __index_level_0__ int64 0 481k |
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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 | 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 | 461,200 |
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 | 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 | 461,201 |
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 | 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 | 461,202 |
def is_cube(self): r""" Returns True if self is a cube, and False otherwise. EXAMPLES:: sage: W = Words('012') sage: W('012012012').is_cube() True sage: W('01010101').is_cube() False sage: W().is_cube() True sage: W('012012').is_cube() False """ if self.length() % 3 != 0: return False l = self.length() / 3 return sel... | def is_cube(self): r""" Returns True if self is a cube, and False otherwise. EXAMPLES:: sage: Word('012012012').is_cube() True sage: Word('01010101').is_cube() False sage: Word().is_cube() True sage: Word('012012').is_cube() False """ if self.length() % 3 != 0: return False l = self.length() / 3 return self[:l] == se... | 461,203 |
def is_cube_free(self): r""" Returns True if self does not contain cubes, and False otherwise. EXAMPLES:: sage: W = Words('123') sage: W('12312').is_cube_free() True sage: W('32221').is_cube_free() False sage: W().is_cube_free() True """ l = self.length() if l < 3: return True suff = self for i in xrange(0, l - 3): f... | def is_cube_free(self): r""" Returns True if self does not contain cubes, and False otherwise. EXAMPLES:: sage: Word('12312').is_cube_free() True sage: Word('32221').is_cube_free() False sage: Word().is_cube_free() True TESTS: We make sure that sage: Word('111').is_cube_free() False sage: Word('2111').is_cube_free... | 461,204 |
def is_cube_free(self): r""" Returns True if self does not contain cubes, and False otherwise. EXAMPLES:: sage: W = Words('123') sage: W('12312').is_cube_free() True sage: W('32221').is_cube_free() False sage: W().is_cube_free() True """ l = self.length() if l < 3: return True suff = self for i in xrange(0, l - 3): f... | def is_cube_free(self): r""" Returns True if self does not contain cubes, and False otherwise. EXAMPLES:: sage: W = Words('123') sage: W('12312').is_cube_free() True sage: W('32221').is_cube_free() False sage: W().is_cube_free() True """ l = self.length() if l < 3: return True for start in xrange(0, L - 2): for end i... | 461,205 |
def is_cube_free(self): r""" Returns True if self does not contain cubes, and False otherwise. EXAMPLES:: sage: W = Words('123') sage: W('12312').is_cube_free() True sage: W('32221').is_cube_free() False sage: W().is_cube_free() True """ l = self.length() if l < 3: return True suff = self for i in xrange(0, l - 3): f... | def is_cube_free(self): r""" Returns True if self does not contain cubes, and False otherwise. EXAMPLES:: sage: W = Words('123') sage: W('12312').is_cube_free() True sage: W('32221').is_cube_free() False sage: W().is_cube_free() True """ l = self.length() if l < 3: return True suff = self for i in xrange(0, l - 3): f... | 461,206 |
def integral(self, x=None, a=None, b=None, definite=False): r""" By default, returns the indefinite integral of the function. If definite=True is given, returns the definite integral. | def integral(self, x=None, a=None, b=None, definite=False): r""" By default, returns the indefinite integral of the function. If definite=True is given, returns the definite integral. | 461,207 |
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun... | def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun... | 461,208 |
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun... | def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun... | 461,209 |
def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun... | def evalunitdict(): """ Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units. EXAMPLES:: sage: sage.symbolic.units.evalun... | 461,210 |
def str_to_unit(name): """ Create the symbolic unit with given name. A symbolic unit is a class that derives from symbolic expression, and has a specialized docstring. INPUT: - ``name`` -- string OUTPUT: - UnitExpression EXAMPLES:: sage: sage.symbolic.units.str_to_unit('acre') acre sage: type(sage.symbolic.unit... | def str_to_unit(name): """ Create the symbolic unit with given name. A symbolic unit is a class that derives from symbolic expression, and has a specialized docstring. INPUT: - ``name`` -- string OUTPUT: - UnitExpression EXAMPLES:: sage: sage.symbolic.units.str_to_unit('acre') acre sage: type(sage.symbolic.unit... | 461,211 |
def __init__(self, data, name=''): """ EXAMPLES:: | def __init__(self, data, name=''): """ EXAMPLES:: | 461,212 |
def __getattr__(self, name): """ Return the unit with the given name. | def __getattr__(self, name): """ Return the unit with the given name. | 461,213 |
def __repr__(self): """ Return string representation of this collection of units. | def __repr__(self): """ Return string representation of this collection of units. | 461,214 |
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. | 461,215 |
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 `... | 461,216 |
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 ... | 461,217 |
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 ... | 461,218 |
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 ... | 461,219 |
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 ... | 461,220 |
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 ... | 461,221 |
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 ... | 461,222 |
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 ... | 461,223 |
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 ... | 461,224 |
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... | 461,225 |
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... | 461,226 |
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... | 461,227 |
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... | 461,228 |
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... | 461,229 |
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... | 461,230 |
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... | 461,231 |
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... | 461,232 |
def __init__(self, s): """ TESTS:: sage: S = Subsets([1,2,3]) sage: S == loads(dumps(S)) True sage: s = Subsets(Set([1])) sage: e = s.first() sage: isinstance(e, s.element_class) True """ self.s = Set(s) | def __init__(self, s): """ TESTS:: sage: S = Subsets([1,2,3]) sage: TestSuite(S).run() sage: s = Subsets(Set([1])) sage: e = s.first() sage: isinstance(e, s.element_class) True """ self.s = Set(s) | 461,233 |
def unrank(self, r): """ Returns the subset of s that has rank k. EXAMPLES:: sage: Subsets(3).unrank(0) {} sage: Subsets([2,4,5]).unrank(1) {2} sage: s = Subsets([2,4,5]) """ | def unrank(self, r): """ Returns the subset of s that has rank k. EXAMPLES:: sage: Subsets(3).unrank(0) {} sage: Subsets([2,4,5]).unrank(1) {2} sage: s = Subsets([2,4,5]) """ | 461,234 |
def unrank(self, r): """ Returns the subset of s that has rank k. EXAMPLES:: sage: Subsets(3).unrank(0) {} sage: Subsets([2,4,5]).unrank(1) {2} sage: s = Subsets([2,4,5]) """ | def unrank(self, r): """ Returns the subset of s that has rank k. EXAMPLES:: sage: Subsets(3).unrank(0) {} sage: Subsets([2,4,5]).unrank(1) {2} sage: s = Subsets([2,4,5]) """ | 461,235 |
def __init__(self, s, k): """ TESTS:: sage: S = Subsets(3,2) sage: S == loads(dumps(S)) True sage: s = Subsets(Set([1])) sage: e = s.first() sage: isinstance(e, s.element_class) True """ self.s = Set(s) self.k = k | def __init__(self, s, k): """ TESTS:: sage: S = Subsets(3,2) sage: TestSuite(S).run() sage: s = Subsets(Set([1])) sage: e = s.first() sage: isinstance(e, s.element_class) True """ self.s = Set(s) self.k = k | 461,236 |
def unrank(self, r): """ Returns the subset of s that has rank k. EXAMPLES:: sage: Subsets(3,2).unrank(0) {1, 2} sage: Subsets([2,4,5],2).unrank(0) {2, 4} """ | def unrank(self, r): """ Returns the subset of s that has rank k. EXAMPLES:: sage: Subsets(3,2).unrank(0) {1, 2} sage: Subsets([2,4,5],2).unrank(0) {2, 4} """ | 461,237 |
def unrank(self, r): """ Returns the subset of s that has rank k. EXAMPLES:: sage: Subsets(3,2).unrank(0) {1, 2} sage: Subsets([2,4,5],2).unrank(0) {2, 4} """ | def unrank(self, r): """ Returns the subset of s that has rank k. EXAMPLES:: sage: Subsets(3,2).unrank(0) {1, 2} sage: Subsets([2,4,5],2).unrank(0) {2, 4} """ | 461,238 |
def unrank(self, r): """ Returns the subset of s that has rank k. EXAMPLES:: sage: Subsets(3,2).unrank(0) {1, 2} sage: Subsets([2,4,5],2).unrank(0) {2, 4} """ | def unrank(self, r): """ Returns the subset of s that has rank k. EXAMPLES:: sage: Subsets(3,2).unrank(0) {1, 2} sage: Subsets([2,4,5],2).unrank(0) {2, 4} """ | 461,239 |
def __iter__(self): """ Iterates through the subsets of the multiset ``self._s``. Note that each subset is represented by a list of its elements rather than a set since we can have multiplicities (no multiset data structure yet in sage). | def __iter__(self): """ Iterates through the subsets of the multiset ``self._s``. Note that each subset is represented by a list of its elements rather than a set since we can have multiplicities (no multiset data structure yet in sage). | 461,240 |
def basiclemmavec(self,M): """ Finds a vector where the value of the quadratic form is coprime to M. EXAMPLES: sage: Q = QuadraticForm(ZZ, 2, [2, 1, 5]) sage: Q.basiclemmavec(10) (6, 5) sage: Q(_) 227 """ V=FreeModule(self.base_ring(),self.dim()) mat = self.matrix() vec = [] mod = [] M0 = abs(M) if M0 == 1: return V(... | def basiclemmavec(self,M): """ Finds a vector where the value of the quadratic form is coprime to M. EXAMPLES: sage: Q = QuadraticForm(ZZ, 2, [2, 1, 5]) sage: Q.basiclemmavec(10) (6, 5) sage: Q(_) 227 """ V=FreeModule(self.base_ring(),self.dim()) mat = self.matrix() vec = [] mod = [] M0 = abs(M) if M0 == 1: return V(... | 461,241 |
def bound_kato(self): r""" Returns a list `p` of primes such that the theorems of Kato's [Ka] and others (e.g., as explained in a paper/thesis of Grigor Grigorov [Gri]) imply that if `p` divides the order of Sha(E) then `p` is in the list. | def bound_kato(self): r""" Returns a list `p` of primes such that the theorems of Kato's [Ka] and others (e.g., as explained in a paper/thesis of Grigor Grigorov [Gri]) imply that if `p` divides the order of Sha(E) then `p` is in the list. | 461,242 |
def bound_kato(self): r""" Returns a list `p` of primes such that the theorems of Kato's [Ka] and others (e.g., as explained in a paper/thesis of Grigor Grigorov [Gri]) imply that if `p` divides the order of Sha(E) then `p` is in the list. | def bound_kato(self): r""" Returns a list `p` of primes such that the theorems of Kato's [Ka] and others (e.g., as explained in a paper/thesis of Grigor Grigorov [Gri]) imply that if `p` divides the order of Sha(E) then `p` is in the list. | 461,243 |
def bound_kato(self): r""" Returns a list `p` of primes such that the theorems of Kato's [Ka] and others (e.g., as explained in a paper/thesis of Grigor Grigorov [Gri]) imply that if `p` divides the order of Sha(E) then `p` is in the list. | def bound_kato(self): r""" Returns a list `p` of primes such that the theorems of Kato's [Ka] and others (e.g., as explained in a paper/thesis of Grigor Grigorov [Gri]) imply that if `p` divides the order of Sha(E) then `p` is in the list. | 461,244 |
def bound_kato(self): r""" Returns a list `p` of primes such that the theorems of Kato's [Ka] and others (e.g., as explained in a paper/thesis of Grigor Grigorov [Gri]) imply that if `p` divides the order of Sha(E) then `p` is in the list. | def bound_kato(self): r""" Returns a list `p` of primes such that the theorems of Kato's [Ka] and others (e.g., as explained in a paper/thesis of Grigor Grigorov [Gri]) imply that if `p` divides the order of Sha(E) then `p` is in the list. | 461,245 |
def map(self, f, name=None): """ Returns the image `\{f(x) x in self\}` of this combinatorial class by `f`, as a combinatorial class. | def map(self, f, name=None): r""" Returns the image `\{f(x) | x \in \text{self}\}` of this combinatorial class by `f`, as a combinatorial class. | 461,246 |
def map(self, f, name=None): """ Returns the image `\{f(x) x in self\}` of this combinatorial class by `f`, as a combinatorial class. | def map(self, f, name=None): """ Returns the image `\{f(x) x in self\}` of this combinatorial class by `f`, as a combinatorial class. | 461,247 |
def map(self, f, name=None): """ Returns the image `\{f(x) x in self\}` of this combinatorial class by `f`, as a combinatorial class. | def map(self, f, name=None): """ Returns the image `\{f(x) x in self\}` of this combinatorial class by `f`, as a combinatorial class. | 461,248 |
def is_prime(n, flag=0): r""" Returns True if `x` is prime, and False otherwise. The result is proven correct - *this is NOT a pseudo-primality test!*. INPUT: - ``flag`` - int - ``0`` (default) - use a combination of algorithms. - ``1`` - certify primality using the Pocklington-Lehmer Test. - ``2`` - certify pri... | def is_prime(n): r""" Returns True if `x` is prime, and False otherwise. The result is proven correct - *this is NOT a pseudo-primality test!*. INPUT: - ``flag`` - int - ``0`` (default) - use a combination of algorithms. - ``1`` - certify primality using the Pocklington-Lehmer Test. - ``2`` - certify primality u... | 461,249 |
def is_prime(n, flag=0): r""" Returns True if `x` is prime, and False otherwise. The result is proven correct - *this is NOT a pseudo-primality test!*. INPUT: - ``flag`` - int - ``0`` (default) - use a combination of algorithms. - ``1`` - certify primality using the Pocklington-Lehmer Test. - ``2`` - certify pri... | def is_prime(n, flag=0): r""" Returns ``True`` if `n` is prime, and ``False`` otherwise. AUTHORS: - Kevin Stueve kstueve@uw.edu (2010-01-17): delegated calculation to ``n.is_prime()`` INPUT: - ``n`` - the object for which to determine primality OUTPUT: - ``bool`` - True or False .. note:: We do not consid... | 461,250 |
def is_prime(n, flag=0): r""" Returns True if `x` is prime, and False otherwise. The result is proven correct - *this is NOT a pseudo-primality test!*. INPUT: - ``flag`` - int - ``0`` (default) - use a combination of algorithms. - ``1`` - certify primality using the Pocklington-Lehmer Test. - ``2`` - certify pri... | def is_prime(n, flag=0): r""" Returns True if `x` is prime, and False otherwise. The result is proven correct - *this is NOT a pseudo-primality test!*. INPUT: - ``flag`` - int - ``0`` (default) - use a combination of algorithms. - ``1`` - certify primality using the Pocklington-Lehmer Test. - ``2`` - certify pri... | 461,251 |
def is_prime(n, flag=0): r""" Returns True if `x` is prime, and False otherwise. The result is proven correct - *this is NOT a pseudo-primality test!*. INPUT: - ``flag`` - int - ``0`` (default) - use a combination of algorithms. - ``1`` - certify primality using the Pocklington-Lehmer Test. - ``2`` - certify pri... | def is_prime(n, flag=0): r""" Returns True if `x` is prime, and False otherwise. The result is proven correct - *this is NOT a pseudo-primality test!*. INPUT: - ``flag`` - int - ``0`` (default) - use a combination of algorithms. - ``1`` - certify primality using the Pocklington-Lehmer Test. - ``2`` - certify pri... | 461,252 |
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... | 461,253 |
def contradicts(self, soln): """ Returns ``True`` if this assumption is violated by the given variable assignment(s). EXAMPLES:: sage: from sage.symbolic.assumptions import GenericDeclaration sage: GenericDeclaration(x, 'integer').contradicts(x==4) False sage: GenericDeclaration(x, 'integer').contradicts(x==4.0) Fals... | def contradicts(self, soln): """ Returns ``True`` if this assumption is violated by the given variable assignment(s). EXAMPLES:: sage: from sage.symbolic.assumptions import GenericDeclaration sage: GenericDeclaration(x, 'integer').contradicts(x==4) False sage: GenericDeclaration(x, 'integer').contradicts(x==4.0) Fals... | 461,254 |
def edge_cut(self, s, t, value_only=True, use_edge_labels=False, vertices=False, solver=None, verbose=0): r""" Returns a minimum edge cut between vertices `s` and `t` represented by a list of edges. | def edge_cut(self, s, t, value_only=True, use_edge_labels=False, vertices=False, solver=None, verbose=0): r""" Returns a minimum edge cut between vertices `s` and `t` represented by a list of edges. | 461,255 |
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`. | 461,256 |
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`. | 461,257 |
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`. | 461,258 |
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`. | 461,259 |
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`. | 461,260 |
def bezier3d(path, **options): """ Draws a 3-dimensional bezier path. Input is similar to bezier_path, but each point in the path and each control point is required to have 3 coordinates. INPUT: - ``path`` - a list of curves, which each is a list of points. See further detail below. - ``thickness`` - (default: 2)... | def bezier3d(path, **options): """ Draws a 3-dimensional bezier path. Input is similar to bezier_path, but each point in the path and each control point is required to have 3 coordinates. INPUT: - ``path`` - a list of curves, which each is a list of points. See further detail below. - ``thickness`` - (default: 2)... | 461,261 |
def bezier3d(path, **options): """ Draws a 3-dimensional bezier path. Input is similar to bezier_path, but each point in the path and each control point is required to have 3 coordinates. INPUT: - ``path`` - a list of curves, which each is a list of points. See further detail below. - ``thickness`` - (default: 2)... | def bezier3d(path, **options): """ Draws a 3-dimensional bezier path. Input is similar to bezier_path, but each point in the path and each control point is required to have 3 coordinates. INPUT: - ``path`` - a list of curves, which each is a list of points. See further detail below. - ``thickness`` - (default: 2)... | 461,262 |
def bezier3d(path, **options): """ Draws a 3-dimensional bezier path. Input is similar to bezier_path, but each point in the path and each control point is required to have 3 coordinates. INPUT: - ``path`` - a list of curves, which each is a list of points. See further detail below. - ``thickness`` - (default: 2)... | def bezier3d(path, **options): """ Draws a 3-dimensional bezier path. Input is similar to bezier_path, but each point in the path and each control point is required to have 3 coordinates. INPUT: - ``path`` - a list of curves, which each is a list of points. See further detail below. - ``thickness`` - (default: 2)... | 461,263 |
def frame3d(lower_left, upper_right, **kwds): """ Draw a frame in 3D. Primarily used as a helper function for creating frames for 3D graphics viewing. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, ... | def frame3d(lower_left, upper_right, **kwds): """ Draw a frame in 3-D. Primarily used as a helper function for creating frames for 3-D graphics viewing. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple... | 461,264 |
def frame3d(lower_left, upper_right, **kwds): """ Draw a frame in 3D. Primarily used as a helper function for creating frames for 3D graphics viewing. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, ... | def frame3d(lower_left, upper_right, **kwds): """ Draw a frame in 3D. Primarily used as a helper function for creating frames for 3D graphics viewing. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector. - ``upper_right`` - the upper right corner of the frame, as a list, tuple,... | 461,265 |
def frame3d(lower_left, upper_right, **kwds): """ Draw a frame in 3D. Primarily used as a helper function for creating frames for 3D graphics viewing. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, ... | def frame3d(lower_left, upper_right, **kwds): """ Draw a frame in 3D. Primarily used as a helper function for creating frames for 3D graphics viewing. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector. - ``upper_right`` - the upper right corner of the frame, as a list, tuple,... | 461,266 |
def frame_labels(lower_left, upper_right, label_lower_left, label_upper_right, eps = 1, **kwds): """ Draw correct labels for a given frame in 3D. Primarily used as a helper function for creating frames for 3D graphics viewing - do not use directly unless you know what you are doing! INPUT: - ``lower_left`` - the low... | def frame_labels(lower_left, upper_right, label_lower_left, label_upper_right, eps = 1, **kwds): """ Draw correct labels for a given frame in 3-D. Primarily used as a helper function for creating frames for 3-D graphics viewing - do not use directly unless you know what you are doing! INPUT: - ``lower_left`` - the l... | 461,267 |
def frame_labels(lower_left, upper_right, label_lower_left, label_upper_right, eps = 1, **kwds): """ Draw correct labels for a given frame in 3D. Primarily used as a helper function for creating frames for 3D graphics viewing - do not use directly unless you know what you are doing! INPUT: - ``lower_left`` - the low... | def frame_labels(lower_left, upper_right, label_lower_left, label_upper_right, eps = 1, **kwds): """ Draw correct labels for a given frame in 3D. Primarily used as a helper function for creating frames for 3D graphics viewing - do not use directly unless you know what you are doing! INPUT: - ``lower_left`` - the low... | 461,268 |
def frame_labels(lower_left, upper_right, label_lower_left, label_upper_right, eps = 1, **kwds): """ Draw correct labels for a given frame in 3D. Primarily used as a helper function for creating frames for 3D graphics viewing - do not use directly unless you know what you are doing! INPUT: - ``lower_left`` - the low... | def frame_labels(lower_left, upper_right, label_lower_left, label_upper_right, eps = 1, **kwds): """ Draw correct labels for a given frame in 3D. Primarily used as a helper function for creating frames for 3D graphics viewing - do not use directly unless you know what you are doing! INPUT: - ``lower_left`` - the low... | 461,269 |
def frame_labels(lower_left, upper_right, label_lower_left, label_upper_right, eps = 1, **kwds): """ Draw correct labels for a given frame in 3D. Primarily used as a helper function for creating frames for 3D graphics viewing - do not use directly unless you know what you are doing! INPUT: - ``lower_left`` - the low... | def frame_labels(lower_left, upper_right, label_lower_left, label_upper_right, eps = 1, **kwds): """ Draw correct labels for a given frame in 3D. Primarily used as a helper function for creating frames for 3D graphics viewing - do not use directly unless you know what you are doing! INPUT: - ``lower_left`` - the low... | 461,270 |
def ruler(start, end, ticks=4, sub_ticks=4, absolute=False, snap=False, **kwds): """ Draw a ruler in 3D, with major and minor ticks. INPUT: - ``start`` - the beginning of the ruler, as a list, tuple, or vector - ``end`` - the end of the ruler, as a list, tuple, or vector - ``ticks`` - (default: 4) the number of maj... | def ruler(start, end, ticks=4, sub_ticks=4, absolute=False, snap=False, **kwds): """ Draw a ruler in 3-D, with major and minor ticks. INPUT: - ``start`` - the beginning of the ruler, as a list, tuple, or vector - ``end`` - the end of the ruler, as a list, tuple, or vector - ``ticks`` - (default: 4) the number of ma... | 461,271 |
def ruler(start, end, ticks=4, sub_ticks=4, absolute=False, snap=False, **kwds): """ Draw a ruler in 3D, with major and minor ticks. INPUT: - ``start`` - the beginning of the ruler, as a list, tuple, or vector - ``end`` - the end of the ruler, as a list, tuple, or vector - ``ticks`` - (default: 4) the number of maj... | def ruler(start, end, ticks=4, sub_ticks=4, absolute=False, snap=False, **kwds): """ Draw a ruler in 3D, with major and minor ticks. INPUT: - ``start`` - the beginning of the ruler, as a list, tuple, or vector. - ``end`` - the end of the ruler, as a list, tuple, or vector. - ``ticks`` - (default: 4) the number of m... | 461,272 |
def ruler(start, end, ticks=4, sub_ticks=4, absolute=False, snap=False, **kwds): """ Draw a ruler in 3D, with major and minor ticks. INPUT: - ``start`` - the beginning of the ruler, as a list, tuple, or vector - ``end`` - the end of the ruler, as a list, tuple, or vector - ``ticks`` - (default: 4) the number of maj... | def ruler(start, end, ticks=4, sub_ticks=4, absolute=False, snap=False, **kwds): """ Draw a ruler in 3D, with major and minor ticks. INPUT: - ``start`` - the beginning of the ruler, as a list, tuple, or vector. - ``end`` - the end of the ruler, as a list, tuple, or vector. - ``ticks`` - (default: 4) the number of m... | 461,273 |
def ruler(start, end, ticks=4, sub_ticks=4, absolute=False, snap=False, **kwds): """ Draw a ruler in 3D, with major and minor ticks. INPUT: - ``start`` - the beginning of the ruler, as a list, tuple, or vector - ``end`` - the end of the ruler, as a list, tuple, or vector - ``ticks`` - (default: 4) the number of maj... | def ruler(start, end, ticks=4, sub_ticks=4, absolute=False, snap=False, **kwds): """ Draw a ruler in 3D, with major and minor ticks. INPUT: - ``start`` - the beginning of the ruler, as a list, tuple, or vector - ``end`` - the end of the ruler, as a list, tuple, or vector - ``ticks`` - (default: 4) the number of maj... | 461,274 |
def ruler(start, end, ticks=4, sub_ticks=4, absolute=False, snap=False, **kwds): """ Draw a ruler in 3D, with major and minor ticks. INPUT: - ``start`` - the beginning of the ruler, as a list, tuple, or vector - ``end`` - the end of the ruler, as a list, tuple, or vector - ``ticks`` - (default: 4) the number of maj... | def ruler(start, end, ticks=4, sub_ticks=4, absolute=False, snap=False, **kwds): """ Draw a ruler in 3D, with major and minor ticks. INPUT: - ``start`` - the beginning of the ruler, as a list, tuple, or vector - ``end`` - the end of the ruler, as a list, tuple, or vector - ``ticks`` - (default: 4) the number of maj... | 461,275 |
def ruler(start, end, ticks=4, sub_ticks=4, absolute=False, snap=False, **kwds): """ Draw a ruler in 3D, with major and minor ticks. INPUT: - ``start`` - the beginning of the ruler, as a list, tuple, or vector - ``end`` - the end of the ruler, as a list, tuple, or vector - ``ticks`` - (default: 4) the number of maj... | def ruler(start, end, ticks=4, sub_ticks=4, absolute=False, snap=False, **kwds): """ Draw a ruler in 3D, with major and minor ticks. INPUT: - ``start`` - the beginning of the ruler, as a list, tuple, or vector - ``end`` - the end of the ruler, as a list, tuple, or vector - ``ticks`` - (default: 4) the number of maj... | 461,276 |
def ruler_frame(lower_left, upper_right, ticks=4, sub_ticks=4, **kwds): """ Draw a frame made of 3D rulers, with major and minor ticks. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, or vector - ``t... | def ruler_frame(lower_left, upper_right, ticks=4, sub_ticks=4, **kwds): """ Draw a frame made of 3-D rulers, with major and minor ticks. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, or vector - ``... | 461,277 |
def ruler_frame(lower_left, upper_right, ticks=4, sub_ticks=4, **kwds): """ Draw a frame made of 3D rulers, with major and minor ticks. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, or vector - ``t... | def ruler_frame(lower_left, upper_right, ticks=4, sub_ticks=4, **kwds): """ Draw a frame made of 3D rulers, with major and minor ticks. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector. - ``upper_right`` - the upper right corner of the frame, as a list, tuple, or vector. - `... | 461,278 |
def ruler_frame(lower_left, upper_right, ticks=4, sub_ticks=4, **kwds): """ Draw a frame made of 3D rulers, with major and minor ticks. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, or vector - ``t... | def ruler_frame(lower_left, upper_right, ticks=4, sub_ticks=4, **kwds): """ Draw a frame made of 3D rulers, with major and minor ticks. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector. - ``upper_right`` - the upper right corner of the frame, as a list, tuple, or vector. - `... | 461,279 |
def ruler_frame(lower_left, upper_right, ticks=4, sub_ticks=4, **kwds): """ Draw a frame made of 3D rulers, with major and minor ticks. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, or vector - ``t... | def ruler_frame(lower_left, upper_right, ticks=4, sub_ticks=4, **kwds): """ Draw a frame made of 3D rulers, with major and minor ticks. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, or vector - ``t... | 461,280 |
def ruler_frame(lower_left, upper_right, ticks=4, sub_ticks=4, **kwds): """ Draw a frame made of 3D rulers, with major and minor ticks. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, or vector - ``t... | def ruler_frame(lower_left, upper_right, ticks=4, sub_ticks=4, **kwds): """ Draw a frame made of 3D rulers, with major and minor ticks. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, or vector - ``t... | 461,281 |
def ruler_frame(lower_left, upper_right, ticks=4, sub_ticks=4, **kwds): """ Draw a frame made of 3D rulers, with major and minor ticks. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, or vector - ``t... | def ruler_frame(lower_left, upper_right, ticks=4, sub_ticks=4, **kwds): """ Draw a frame made of 3D rulers, with major and minor ticks. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, or vector - ``t... | 461,282 |
def text3d(txt, (x,y,z), **kwds): r""" Display 3d text. INPUT: - ``txt`` - some text - ``(x,y,z)`` - position - ``**kwds`` - standard 3d graphics options .. note:: There is no way to change the font size or opacity yet. EXAMPLES: We write the word Sage in red at position (1,2,3):: sage: text3d("Sage", (1,2... | def text3d(txt, (x,y,z), **kwds): r""" Display 3d text. INPUT: - ``txt`` - some text - ``(x,y,z)`` - position - ``**kwds`` - standard 3d graphics options .. note:: There is no way to change the font size or opacity yet. EXAMPLES: We write the word Sage in red at position (1,2,3):: sage: text3d("Sage", (1,2... | 461,283 |
def text3d(txt, (x,y,z), **kwds): r""" Display 3d text. INPUT: - ``txt`` - some text - ``(x,y,z)`` - position - ``**kwds`` - standard 3d graphics options .. note:: There is no way to change the font size or opacity yet. EXAMPLES: We write the word Sage in red at position (1,2,3):: sage: text3d("Sage", (1,2... | deftext3d(txt,(x,y,z),**kwds):r"""Display3dtext.INPUT:-``txt``-sometext-``(x,y,z)``-position-``**kwds``-standard3dgraphicsoptions..note::Thereisnowaytochangethefontsizeoropacityyet.EXAMPLES:WewritethewordSageinredatposition(1,2,3)::sage:text3d("Sage",(1,2,3),color=(0.5,0,0))Wedrawamulticolorspiralofnumbers::sage:sum([t... | 461,284 |
def __init__(self, center, size=1, **kwds): """ Create the graphics primitive :class:`Point` in 3D. See the docstring of this class for full documentation. | def __init__(self, center, size=1, **kwds): """ Create the graphics primitive :class:`Point` in 3-D. See the docstring of this class for full documentation. | 461,285 |
def bounding_box(self): """ Returns the lower and upper corners of a 3D bounding box for self. This is used for rendering and self should fit entirely within this box. In this case, we simply return the center of the point. | def bounding_box(self): """ Returns the lower and upper corners of a 3-D bounding box for ``self``. This is used for rendering and ``self`` should fit entirely within this box. In this case, we simply return the center of the point. | 461,286 |
def tachyon_repr(self, render_params): """ Returns representation of the point suitable for plotting using Tachyon ray tracer. | def tachyon_repr(self, render_params): """ Returns representation of the point suitable for plotting using Tachyon ray tracer. | 461,287 |
def __init__(self, points, thickness=5, corner_cutoff=.5, arrow_head=False, **kwds): """ Create the graphics primitive :class:`Line` in 3D. See the docstring of this class for full documentation. | def __init__(self, points, thickness=5, corner_cutoff=.5, arrow_head=False, **kwds): """ Create the graphics primitive :class:`Line` in 3-D. See the docstring of this class for full documentation. | 461,288 |
def bounding_box(self): """ Returns the lower and upper corners of a 3D bounding box for self. This is used for rendering and self should fit entirely within this box. In this case, we return the highest and lowest values of each coordinate among all points. | def bounding_box(self): """ Returns the lower and upper corners of a 3-D bounding box for ``self``. This is used for rendering and ``self`` should fit entirely within this box. In this case, we return the highest and lowest values of each coordinate among all points. | 461,289 |
def tachyon_repr(self, render_params): """ Returns representation of the line suitable for plotting using Tachyon ray tracer. | def tachyon_repr(self, render_params): """ Returns representation of the line suitable for plotting using Tachyon ray tracer. | 461,290 |
def __init__(self, deprecated=None, **renames): """ A decorator which renames keyword arguments and optionally deprecates the new keyword. INPUT: - ``deprecated`` - If the option being renamed is deprecated, this is the Sage version where the deprecation initially occurs. - the rest of the arguments is a list of keyw... | def __init__(self, deprecated=None, **renames): """ A decorator which renames keyword arguments and optionally deprecates the new keyword. INPUT: - ``deprecated`` - If the option being renamed is deprecated, this is the Sage version where the deprecation initially occurs. - the rest of the arguments is a list of keyw... | 461,291 |
def __init__(self, deprecated=None, **renames): """ A decorator which renames keyword arguments and optionally deprecates the new keyword. INPUT: - ``deprecated`` - If the option being renamed is deprecated, this is the Sage version where the deprecation initially occurs. - the rest of the arguments is a list of keyw... | def __init__(self, deprecated=None, **renames): """ A decorator which renames keyword arguments and optionally deprecates the new keyword. INPUT: - ``deprecated`` - If the option being renamed is deprecated, this is the Sage version where the deprecation initially occurs. - the rest of the arguments is a list of key... | 461,292 |
def __init__(self, deprecated=None, **renames): """ A decorator which renames keyword arguments and optionally deprecates the new keyword. INPUT: - ``deprecated`` - If the option being renamed is deprecated, this is the Sage version where the deprecation initially occurs. - the rest of the arguments is a list of keyw... | def__init__(self,deprecated=None,**renames):"""Adecoratorwhichrenameskeywordargumentsandoptionallydeprecatesthenewkeyword.INPUT:-``deprecated``-Iftheoptionbeingrenamedisdeprecated,thisistheSageversionwherethedeprecationinitiallyoccurs.-therestoftheargumentsisalistofkeywordargumentsintheform``renamed_option='existing_op... | 461,293 |
def basiclemmavec(self,M): """ Finds a vector where the value of the quadratic form is coprime to M. EXAMPLES: sage: Q = QuadraticForm(ZZ, 2, [2, 1, 5]) sage: Q.basiclemmavec(10) (6, 5) sage: Q(_) 227 """ V=FreeModule(self.base_ring(),self.dim()) mat = self.matrix() vec = [] mod = [] M0 = abs(M) if M0 == 1: return V(... | def basiclemmavec(self,M): """ Finds a vector where the value of the quadratic form is coprime to M. EXAMPLES: sage: Q = QuadraticForm(ZZ, 2, [2, 1, 5]) sage: Q.basiclemmavec(10) (6, 5) sage: Q(_) 227 """ V=FreeModule(self.base_ring(),self.dim()) mat = self.matrix() vec = [] mod = [] M0 = abs(M) if M0 == 1: return V(... | 461,294 |
def __init__(self): r""" The inverse of the hyperbolic secant function. | def __init__(self): r""" The inverse of the hyperbolic secant function. | 461,295 |
def _pcubicroots(b, c, d): r""" Local function returning the number of roots of `x^3 + b*x^2 + c*x + d` modulo `P`, counting multiplicities """ return sum([rr[1] for rr in PolynomialRing(F, 'x')([d, c, b, 1]).roots()],0) | def _pcubicroots(b, c, d): r""" Local function returning the number of roots of `x^3 + b*x^2 + c*x + d` modulo `P`, counting multiplicities """ return sum([rr[1] for rr in PolynomialRing(F, 'x')([d, c, b, 1]).roots()],0) | 461,296 |
def steiner_tree(self,vertices, weighted = False): r""" Returns a tree of minimum weight connecting the given set of vertices. | def steiner_tree(self,vertices, weighted = False): r""" Returns a tree of minimum weight connecting the given set of vertices. | 461,297 |
def steiner_tree(self,vertices, weighted = False): r""" Returns a tree of minimum weight connecting the given set of vertices. | def steiner_tree(self,vertices, weighted = False): r""" Returns a tree of minimum weight connecting the given set of vertices. | 461,298 |
def steiner_tree(self,vertices, weighted = False): r""" Returns a tree of minimum weight connecting the given set of vertices. | def steiner_tree(self,vertices, weighted = False): r""" Returns a tree of minimum weight connecting the given set of vertices. | 461,299 |
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