bugged stringlengths 4 228k | fixed stringlengths 0 96.3M | __index_level_0__ int64 0 481k |
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def induced_subgraph_search(self, G): r""" Returns an induced copy of `G` in self. | def induced_subgraph_search(self, G): r""" Returns an induced copy of `G` in self. | 460,700 |
def induced_subgraph_search(self, G): r""" Returns an induced copy of `G` in self. | def induced_subgraph_search(self, G): r""" Returns an induced copy of `G` in self. | 460,701 |
def induced_subgraph_search(self, G): r""" Returns an induced copy of `G` in self. | def induced_subgraph_search(self, G): r""" Returns an induced copy of `G` in self. | 460,702 |
def induced_subgraph_search(self, G): r""" Returns an induced copy of `G` in self. | def induced_subgraph_search(self, G): r""" Returns an induced copy of `G` in self. | 460,703 |
def induced_subgraph_search(self, G): r""" Returns an induced copy of `G` in self. | def induced_subgraph_search(self, G): r""" Returns an induced copy of `G` in self. | 460,704 |
def induced_subgraph_search(self, G): r""" Returns an induced copy of `G` in self. | def induced_subgraph_search(self, G): r""" Returns an induced copy of `G` in self. | 460,705 |
def induced_subgraph_search(self, G): r""" Returns an induced copy of `G` in self. | def induced_subgraph_search(self, G): r""" Returns an induced copy of `G` in self. | 460,706 |
def valuation(m, p): """ The exact power of p that divides m. m should be an integer or rational (but maybe other types work too.) This actually just calls the m.valuation() method. If m is 0, this function returns rings.infinity. EXAMPLES:: sage: valuation(512,2) 9 sage: valuation(1,2) 0 sage: valuation(5/9, 3) -... | def valuation(m,*args1, **args2): """ This actually just calls the m.valuation() method. See the documentation of m.valuation() for a more precise description. Use of this function by developers is discouraged. Use m.valuation() instead. .. NOTE:: This is not always a valuation in the mathematical sense. For more inf... | 460,707 |
def valuation(m, p): """ The exact power of p that divides m. m should be an integer or rational (but maybe other types work too.) This actually just calls the m.valuation() method. If m is 0, this function returns rings.infinity. EXAMPLES:: sage: valuation(512,2) 9 sage: valuation(1,2) 0 sage: valuation(5/9, 3) -... | def valuation(m, p): """ The exact power of p that divides m. m should be an integer or rational (but maybe other types work too.) This actually just calls the m.valuation() method. If m is 0, this function returns rings.infinity. EXAMPLES:: sage: valuation(512,2) 9 sage: valuation(1,2) 0 sage: valuation(5/9, 3) -... | 460,708 |
def integral(f, *args, **kwds): r""" The integral of `f`. EXAMPLES:: sage: integral(sin(x), x) -cos(x) sage: integral(sin(x)^2, x, pi, 123*pi/2) 121/4*pi sage: integral( sin(x), x, 0, pi) 2 We integrate a symbolic function:: sage: f(x,y,z) = x*y/z + sin(z) sage: integral(f, z) (x, y, z) |--> x*y*log(z) - cos(z) ::... | def integral(f, *args, **kwds): r""" The integral of `f`. EXAMPLES:: sage: integral(sin(x), x) -cos(x) sage: integral(sin(x)^2, x, pi, 123*pi/2) 121/4*pi sage: integral( sin(x), x, 0, pi) 2 We integrate a symbolic function:: sage: f(x,y,z) = x*y/z + sin(z) sage: integral(f, z) (x, y, z) |--> x*y*log(z) - cos(z) ::... | 460,709 |
def is_submodule(self, other): """ Return True if self is a submodule of other. EXAMPLES:: sage: M = FreeModule(ZZ,3) sage: V = M.ambient_vector_space() sage: X = V.span([[1/2,1/2,0],[1/2,0,1/2]], ZZ) sage: Y = V.span([[1,1,1]], ZZ) sage: N = X + Y sage: M.is_submodule(X) False sage: M.is_submodule(Y) False sage: Y.i... | def is_submodule(self, other): """ Return True if self is a submodule of other. EXAMPLES:: sage: M = FreeModule(ZZ,3) sage: V = M.ambient_vector_space() sage: X = V.span([[1/2,1/2,0],[1/2,0,1/2]], ZZ) sage: Y = V.span([[1,1,1]], ZZ) sage: N = X + Y sage: M.is_submodule(X) False sage: M.is_submodule(Y) False sage: Y.i... | 460,710 |
def Tableau(t): """ Returns the tableau object corresponding to t. Note that Sage uses the English convention for partitions and tableaux. EXAMPLES:: sage: t = Tableau([[1,2,3],[4,5]]); t [[1, 2, 3], [4, 5]] sage: t.shape() [3, 2] sage: t.is_standard() True """ if isinstance(t, Tableau_class): return t elif t in Tab... | def Tableau(t): """ Returns the tableau object corresponding to t. A tableau in sage is a finite list of lists, whose lengths are weakly decreasing, or an empty list, representing the empty tableau. The entries of a tableau can be any sage object. Note that Sage uses the English convention for partitions and tableau... | 460,711 |
def anti_restrict(self, n): """ Returns the skew tableau formed by removing all of the cells from self that are filled with a number less than EXAMPLES:: sage: t = Tableau([[1,2,3],[4,5]]); t [[1, 2, 3], [4, 5]] sage: t.anti_restrict(1) [[None, 2, 3], [4, 5]] sage: t.anti_restrict(2) [[None, None, 3], [4, 5]] sage: t... | def anti_restrict(self, n): """ Returns the skew tableau formed by removing all of the cells from self that are filled with a number less than `n`. EXAMPLES:: sage: t = Tableau([[1,2,3],[4,5]]); t [[1, 2, 3], [4, 5]] sage: t.anti_restrict(1) [[None, 2, 3], [4, 5]] sage: t.anti_restrict(2) [[None, None, 3], [4, 5]] sa... | 460,712 |
def up(self): """ An iterator for all the tableaux that can be obtained from self by adding a cell. EXAMPLES:: sage: t = Tableau([[1,2]]) sage: [x for x in t.up()] [[[1, 2, 3]], [[1, 2], [3]]] """ #Get a list of all places where we can add a cell #to the shape of self outside_corners = self.shape().outside_corners() | def up(self): """ An iterator for all the tableaux that can be obtained from self by adding a cell. EXAMPLES:: sage: t = Tableau([[1,2]]) sage: [x for x in t.up()] [[[1, 2, 3]], [[1, 2], [3]]] """ #Get a list of all places where we can add a cell #to the shape of self outside_corners = self.shape().outside_corners() | 460,713 |
def Tableaux(n=None): """ Returns the combinatorial class of tableaux. If n is specified, then it returns the combinatorial class of all tableaux of size n. EXAMPLES:: sage: T = Tableaux(); T Tableaux sage: [[1,2],[3,4]] in T True sage: [[1,2],[3]] in T True sage: [1,2,3] in T False :: sage: T = Tableaux(4); T Tabl... | def Tableaux(n=None): """ Returns the combinatorial class of tableaux. If n is specified, then it returns the combinatorial class of all tableaux of size n. A tableau in sage is a finite list of lists, whose lengths are weakly decreasing. The entries can be anything at all. EXAMPLES:: sage: T = Tableaux(); T Tablea... | 460,714 |
def Tableaux(n=None): """ Returns the combinatorial class of tableaux. If n is specified, then it returns the combinatorial class of all tableaux of size n. EXAMPLES:: sage: T = Tableaux(); T Tableaux sage: [[1,2],[3,4]] in T True sage: [[1,2],[3]] in T True sage: [1,2,3] in T False :: sage: T = Tableaux(4); T Tabl... | def Tableaux(n=None): """ Returns the combinatorial class of tableaux. If n is specified, then it returns the combinatorial class of all tableaux of size n. EXAMPLES:: sage: T = Tableaux(); T Tableaux sage: [[1,2],[3,4]] in T True sage: [[1,2],[3]] in T True :: sage: T = Tableaux(4); T Tableaux of size 4 sage: [[1,... | 460,715 |
def __repr__(self): """ TESTS:: sage: repr(Tableaux()) 'Tableaux' """ return "Tableaux" | def _repr_(self): """ TESTS:: sage: repr(Tableaux()) 'Tableaux' """ return "Tableaux" | 460,716 |
def __repr__(self): """ TESTS:: sage: repr(Tableaux(4)) 'Tableaux of size 4' """ return "Tableaux of size %s"%self.n | def _repr_(self): """ TESTS:: sage: repr(Tableaux(4)) 'Tableaux of size 4' """ return "Tableaux of size %s"%self.n | 460,717 |
def __repr__(self): """ TESTS:: sage: repr(StandardTableaux()) 'Standard tableaux' """ return "Standard tableaux" | def _repr_(self): """ TESTS:: sage: repr(StandardTableaux()) 'Standard tableaux' """ return "Standard tableaux" | 460,718 |
def __repr__(self): """ TESTS:: sage: repr(StandardTableaux(3)) 'Standard tableaux of size 3' """ return "Standard tableaux of size %s"%self.n | def _repr_(self): """ TESTS:: sage: repr(StandardTableaux(3)) 'Standard tableaux of size 3' """ return "Standard tableaux of size %s"%self.n | 460,719 |
def __repr__(self): """ TESTS:: sage: repr(StandardTableaux([2,1,1])) 'Standard tableaux of shape [2, 1, 1]' """ return "Standard tableaux of shape %s"%str(self.p) | def _repr_(self): """ TESTS:: sage: repr(StandardTableaux([2,1,1])) 'Standard tableaux of shape [2, 1, 1]' """ return "Standard tableaux of shape %s"%str(self.p) | 460,720 |
def SemistandardTableaux(p=None, mu=None): """ Returns the combinatorial class of semistandard tableaux. If p is specified and is a partition, then it returns the class of semistandard tableaux of shape p (and max entry sum(p)) If p is specified and is an integer, it returns the class of semistandard tableaux of size... | def SemistandardTableaux(p=None, mu=None, max_entry=None): """ Returns the combinatorial class of semistandard tableaux. If p is specified and is a partition, then it returns the class of semistandard tableaux of shape p (and max entry sum(p)) If p is specified and is an integer, it returns the class of semistandard ... | 460,721 |
def SemistandardTableaux(p=None, mu=None): """ Returns the combinatorial class of semistandard tableaux. If p is specified and is a partition, then it returns the class of semistandard tableaux of shape p (and max entry sum(p)) If p is specified and is an integer, it returns the class of semistandard tableaux of size... | def SemistandardTableaux(p=None, mu=None): """ Returns the combinatorial class of semistandard tableaux. If p is specified and is a partition, then it returns the class of semistandard tableaux of shape p. If p is specified and is an integer, it returns the class of semistandard tableaux of size p. If mu is also spe... | 460,722 |
def SemistandardTableaux(p=None, mu=None): """ Returns the combinatorial class of semistandard tableaux. If p is specified and is a partition, then it returns the class of semistandard tableaux of shape p (and max entry sum(p)) If p is specified and is an integer, it returns the class of semistandard tableaux of size... | def SemistandardTableaux(p=None, mu=None): """ Returns the combinatorial class of semistandard tableaux. If p is specified and is a partition, then it returns the class of semistandard tableaux of shape p (and max entry sum(p)) If p is specified and is an integer, it returns the class of semistandard tableaux of size... | 460,723 |
def SemistandardTableaux(p=None, mu=None): """ Returns the combinatorial class of semistandard tableaux. If p is specified and is a partition, then it returns the class of semistandard tableaux of shape p (and max entry sum(p)) If p is specified and is an integer, it returns the class of semistandard tableaux of size... | def SemistandardTableaux(p=None, mu=None): """ Returns the combinatorial class of semistandard tableaux. If p is specified and is a partition, then it returns the class of semistandard tableaux of shape p (and max entry sum(p)) If p is specified and is an integer, it returns the class of semistandard tableaux of size... | 460,724 |
def SemistandardTableaux(p=None, mu=None): """ Returns the combinatorial class of semistandard tableaux. If p is specified and is a partition, then it returns the class of semistandard tableaux of shape p (and max entry sum(p)) If p is specified and is an integer, it returns the class of semistandard tableaux of size... | def SemistandardTableaux(p=None, mu=None): """ Returns the combinatorial class of semistandard tableaux. If p is specified and is a partition, then it returns the class of semistandard tableaux of shape p (and max entry sum(p)) If p is specified and is an integer, it returns the class of semistandard tableaux of size... | 460,725 |
def SemistandardTableaux(p=None, mu=None): """ Returns the combinatorial class of semistandard tableaux. If p is specified and is a partition, then it returns the class of semistandard tableaux of shape p (and max entry sum(p)) If p is specified and is an integer, it returns the class of semistandard tableaux of size... | def SemistandardTableaux(p=None, mu=None): """ Returns the combinatorial class of semistandard tableaux. If p is specified and is a partition, then it returns the class of semistandard tableaux of shape p (and max entry sum(p)) If p is specified and is an integer, it returns the class of semistandard tableaux of size... | 460,726 |
def SemistandardTableaux(p=None, mu=None): """ Returns the combinatorial class of semistandard tableaux. If p is specified and is a partition, then it returns the class of semistandard tableaux of shape p (and max entry sum(p)) If p is specified and is an integer, it returns the class of semistandard tableaux of size... | def SemistandardTableaux(p=None, mu=None): """ Returns the combinatorial class of semistandard tableaux. If p is specified and is a partition, then it returns the class of semistandard tableaux of shape p (and max entry sum(p)) If p is specified and is an integer, it returns the class of semistandard tableaux of size... | 460,727 |
def SemistandardTableaux(p=None, mu=None): """ Returns the combinatorial class of semistandard tableaux. If p is specified and is a partition, then it returns the class of semistandard tableaux of shape p (and max entry sum(p)) If p is specified and is an integer, it returns the class of semistandard tableaux of size... | def SemistandardTableaux(p=None, mu=None): """ Returns the combinatorial class of semistandard tableaux. If p is specified and is a partition, then it returns the class of semistandard tableaux of shape p (and max entry sum(p)) If p is specified and is an integer, it returns the class of semistandard tableaux of size... | 460,728 |
def SemistandardTableaux(p=None, mu=None): """ Returns the combinatorial class of semistandard tableaux. If p is specified and is a partition, then it returns the class of semistandard tableaux of shape p (and max entry sum(p)) If p is specified and is an integer, it returns the class of semistandard tableaux of size... | def SemistandardTableaux(p=None, mu=None): """ Returns the combinatorial class of semistandard tableaux. If p is specified and is a partition, then it returns the class of semistandard tableaux of shape p (and max entry sum(p)) If p is specified and is an integer, it returns the class of semistandard tableaux of size... | 460,729 |
def SemistandardTableaux(p=None, mu=None): """ Returns the combinatorial class of semistandard tableaux. If p is specified and is a partition, then it returns the class of semistandard tableaux of shape p (and max entry sum(p)) If p is specified and is an integer, it returns the class of semistandard tableaux of size... | def SemistandardTableaux(p=None, mu=None): """ Returns the combinatorial class of semistandard tableaux. If p is specified and is a partition, then it returns the class of semistandard tableaux of shape p (and max entry sum(p)) If p is specified and is an integer, it returns the class of semistandard tableaux of size... | 460,730 |
def __init__(self): """ TESTS:: sage: SST = SemistandardTableaux() sage: SST == loads(dumps(SST)) True """ | def __init__(self, max_entry=None): """ TESTS:: sage: SST = SemistandardTableaux() sage: SST == loads(dumps(SST)) True """ | 460,731 |
def __init__(self): """ TESTS:: sage: SST = SemistandardTableaux() sage: SST == loads(dumps(SST)) True """ | def __init__(self): """ TESTS:: sage: SST = SemistandardTableaux() sage: SST == loads(dumps(SST)) True """ | 460,732 |
def __contains__(self, x): """ TESTS:: sage: [[1,2],[1]] in SemistandardTableaux() False sage: SST = SemistandardTableaux() sage: all([st in SST for st in StandardTableaux(4)]) True sage: [[1,1],[2]] in SemistandardTableaux() True """ if x not in Tableaux(): return False else: t = Tableau(x) #Check to make sure the f... | def __contains__(self, x): """ TESTS:: sage: [[1,2],[1]] in SemistandardTableaux() False sage: SST = SemistandardTableaux() sage: all([st in SST for st in StandardTableaux(4)]) True sage: [[1,1],[5]] in SemistandardTableaux(max_entry=4) False """ if x not in Tableaux(): return False else: t = Tableau(x) #Check to m... | 460,733 |
def __contains__(self, x): """ TESTS:: sage: [[1,2],[1]] in SemistandardTableaux() False sage: SST = SemistandardTableaux() sage: all([st in SST for st in StandardTableaux(4)]) True sage: [[1,1],[2]] in SemistandardTableaux() True """ if x not in Tableaux(): return False else: t = Tableau(x) #Check to make sure the f... | def __contains__(self, x): """ TESTS:: sage: [[1,2],[1]] in SemistandardTableaux() False sage: SST = SemistandardTableaux() sage: all([st in SST for st in StandardTableaux(4)]) True sage: [[1,1],[2]] in SemistandardTableaux() True """ if x not in Tableaux(): return False else: t = Tableau(x) #Check to make sure the f... | 460,734 |
def __contains__(self, x): """ TESTS:: sage: [[1,2],[1]] in SemistandardTableaux() False sage: SST = SemistandardTableaux() sage: all([st in SST for st in StandardTableaux(4)]) True sage: [[1,1],[2]] in SemistandardTableaux() True """ if x not in Tableaux(): return False else: t = Tableau(x) #Check to make sure the f... | def __contains__(self, x): """ TESTS:: sage: [[1,2],[1]] in SemistandardTableaux() False sage: SST = SemistandardTableaux() sage: all([st in SST for st in StandardTableaux(4)]) True sage: [[1,1],[2]] in SemistandardTableaux() True """ if x not in Tableaux(): return False else: t = Tableau(x) #Check to make sure the f... | 460,735 |
def __contains__(self, x): """ TESTS:: sage: [[1,2],[1]] in SemistandardTableaux() False sage: SST = SemistandardTableaux() sage: all([st in SST for st in StandardTableaux(4)]) True sage: [[1,1],[2]] in SemistandardTableaux() True """ if x not in Tableaux(): return False else: t = Tableau(x) #Check to make sure the f... | def __contains__(self, x): """ TESTS:: sage: [[1,2],[1]] in SemistandardTableaux() False sage: SST = SemistandardTableaux() sage: all([st in SST for st in StandardTableaux(4)]) True sage: [[1,1],[2]] in SemistandardTableaux() True """ if x not in Tableaux(): return False else: t = Tableau(x) #Check to make sure the f... | 460,736 |
def __init__(self, n): """ TESTS:: sage: SST = SemistandardTableaux(3) sage: SST == loads(dumps(SST)) True """ self.n = n | def __init__(self, n, max_entry=None): """ TESTS:: sage: SST = SemistandardTableaux(3) sage: SST == loads(dumps(SST)) True """ self.n = n | 460,737 |
def __repr__(self): """ TESTS:: sage: repr(SemistandardTableaux(3)) 'Semistandard tableaux of size 3' """ return "Semistandard tableaux of size %s"%str(self.n) | self.max_entry = None if max_entry is None: self.max_entry = n else: self.max_entry = max_entry def _repr_(self): """ TESTS:: sage: repr(SemistandardTableaux(3)) 'Semistandard tableaux of size 3' """ return "Semistandard tableaux of size %s"%str(self.n) | 460,738 |
def __repr__(self): """ TESTS:: sage: repr(SemistandardTableaux(3)) 'Semistandard tableaux of size 3' """ return "Semistandard tableaux of size %s"%str(self.n) | def __repr__(self): """ TESTS:: sage: repr(SemistandardTableaux(3)) 'Semistandard tableaux of size 3' """ return "Semistandard tableaux of size %s"%str(self.n) | 460,739 |
def __contains__(self, x): """ EXAMPLES:: sage: [[1,2],[3,3]] in SemistandardTableaux(3) False sage: [[1,2],[3,3]] in SemistandardTableaux(4) True sage: SST = SemistandardTableaux(4) sage: all([sst in SST for sst in SST]) True """ return x in SemistandardTableaux() and sum(map(len, x)) == self.n | def __contains__(self, x): """ EXAMPLES:: sage: [[1,2],[3,3]] in SemistandardTableaux(3) False sage: [[1,2],[3,3]] in SemistandardTableaux(4) True sage: SST = SemistandardTableaux(4) sage: all([sst in SST for sst in SST]) True """ return x in SemistandardTableaux() and sum(map(len, x)) == self.n | 460,740 |
def cardinality(self): """ EXAMPLES:: sage: SemistandardTableaux(3).cardinality() 19 sage: SemistandardTableaux(4).cardinality() 116 sage: ns = range(1, 6) sage: ssts = [ SemistandardTableaux(n) for n in ns ] sage: all([sst.cardinality() == len(sst.list()) for sst in ssts]) True """ c = 0 for part in partition.Partiti... | def cardinality(self): """ EXAMPLES:: sage: SemistandardTableaux(3).cardinality() 19 sage: SemistandardTableaux(4).cardinality() 116 sage: ns = range(1, 6) sage: ssts = [ SemistandardTableaux(n) for n in ns ] sage: all([sst.cardinality() == len(sst.list()) for sst in ssts]) True """ c = 0 for part in partition.Partiti... | 460,741 |
def __iter__(self): """ EXAMPLES:: sage: [ t for t in SemistandardTableaux(2) ] [[[1, 1]], [[1, 2]], [[2, 2]], [[1], [2]]] sage: [ t for t in SemistandardTableaux(3) ] [[[1, 1, 1]], [[1, 1, 2]], [[1, 1, 3]], [[1, 2, 2]], [[1, 2, 3]], [[1, 3, 3]], [[2, 2, 2]], [[2, 2, 3]], [[2, 3, 3]], [[3, 3, 3]], [[1, 1], [2]], [[1, ... | def __iter__(self): """ EXAMPLES:: sage: [ t for t in SemistandardTableaux(2) ] [[[1, 1]], [[1, 2]], [[2, 2]], [[1], [2]]] sage: [ t for t in SemistandardTableaux(3) ] [[[1, 1, 1]], [[1, 1, 2]], [[1, 1, 3]], [[1, 2, 2]], [[1, 2, 3]], [[1, 3, 3]], [[2, 2, 2]], [[2, 2, 3]], [[2, 3, 3]], [[3, 3, 3]], [[1, 1], [2]], [[1, ... | 460,742 |
def __repr__(self): """ TESTS:: sage: repr(SemistandardTableaux([2,1],[2,1])) 'Semistandard tableaux of shape [2, 1] and evaluation [2, 1]' """ return "Semistandard tableaux of shape %s and evaluation %s"%(self.p, self.mu) | def _repr_(self): """ TESTS:: sage: repr(SemistandardTableaux([2,1],[2,1])) 'Semistandard tableaux of shape [2, 1] and evaluation [2, 1]' """ return "Semistandard tableaux of shape %s and evaluation %s"%(self.p, self.mu) | 460,743 |
def __contains__(self, x): """ EXAMPLES:: sage: SST = SemistandardTableaux([2,1], [2,1]) sage: all([sst in SST for sst in SST]) True sage: len(filter(lambda x: x in SST, SemistandardTableaux(3))) 1 sage: SST.cardinality() 1 """ if not x in SemistandardTableaux(self.p): return False n = sum(self.p) | def __contains__(self, x): """ EXAMPLES:: sage: SST = SemistandardTableaux([2,1], [2,1]) sage: all([sst in SST for sst in SST]) True sage: len(filter(lambda x: x in SST, SemistandardTableaux(3))) 1 sage: SST.cardinality() 1 """ if x not in SemistandardTableaux_p(self.p, self.max_entry): return False n = sum(self.p) | 460,744 |
def __init__(self, p): """ TESTS:: sage: SST = SemistandardTableaux([2,1]) sage: SST == loads(dumps(SST)) True """ self.p = p | def __init__(self, p, max_entry=None): """ TESTS:: sage: SST = SemistandardTableaux([2,1]) sage: SST == loads(dumps(SST)) True """ self.p = p | 460,745 |
def __contains__(self, x): """ EXAMPLES:: sage: SST = SemistandardTableaux([2,1]) sage: all([sst in SST for sst in SST]) True sage: len(filter(lambda x: x in SST, SemistandardTableaux(3))) 8 sage: SST.cardinality() 8 """ return x in SemistandardTableaux_all() and map(len, x) == self.p | def __contains__(self, x): """ EXAMPLES:: sage: SST = SemistandardTableaux([2,1]) sage: all([sst in SST for sst in SST]) True sage: len(filter(lambda x: x in SST, SemistandardTableaux(3))) 8 sage: SST.cardinality() 8 """ return x in SemistandardTableaux_all() and map(len, x) == self.p | 460,746 |
def __repr__(self): """ TESTS:: sage: repr(SemistandardTableaux([2,1])) 'Semistandard tableaux of shape [2, 1]' """ return "Semistandard tableaux of shape %s" % str(self.p) | def __repr__(self): """ TESTS:: sage: repr(SemistandardTableaux([2,1])) 'Semistandard tableaux of shape [2, 1]' """ return "Semistandard tableaux of shape %s" % str(self.p) | 460,747 |
def cardinality(self): """ EXAMPLES:: sage: SemistandardTableaux([2,1]).cardinality() 8 sage: SemistandardTableaux([2,2,1]).cardinality() 75 sage: s = SFASchur(QQ) sage: s([2,2,1]).expand(5)(1,1,1,1,1) 75 sage: SemistandardTableaux([5]).cardinality() 126 sage: SemistandardTableaux([3,2,1]).cardinality() 896 """ c = 0 ... | def cardinality(self): """ EXAMPLES:: sage: SemistandardTableaux([2,1]).cardinality() 8 sage: SemistandardTableaux([2,2,1]).cardinality() 75 sage: s = SFASchur(QQ) sage: s([2,2,1]).expand(5)(1,1,1,1,1) 75 sage: SemistandardTableaux([5]).cardinality() 126 sage: SemistandardTableaux([3,2,1]).cardinality() 896 """ c = 0 ... | 460,748 |
def __iter__(self): """ An iterator for the semistandard partitions of shape p. EXAMPLES:: sage: [ t for t in SemistandardTableaux([3]) ] [[[1, 1, 1]], [[1, 1, 2]], [[1, 1, 3]], [[1, 2, 2]], [[1, 2, 3]], [[1, 3, 3]], [[2, 2, 2]], [[2, 2, 3]], [[2, 3, 3]], [[3, 3, 3]]] sage: [ t for t in SemistandardTableaux([2,1]) ] ... | def __iter__(self): """ An iterator for the semistandard partitions of shape p. EXAMPLES:: sage: [ t for t in SemistandardTableaux([3]) ] [[[1, 1, 1]], [[1, 1, 2]], [[1, 1, 3]], [[1, 2, 2]], [[1, 2, 3]], [[1, 3, 3]], [[2, 2, 2]], [[2, 2, 3]], [[2, 3, 3]], [[3, 3, 3]]] sage: [ t for t in SemistandardTableaux([2,1]) ] ... | 460,749 |
def __init__(self, n, mu): """ TESTS:: sage: SST = SemistandardTableaux(3, [2,1]) sage: SST == loads(dumps(SST)) True """ self.n = n self.mu = mu | def __init__(self, n, mu): """ TESTS:: sage: SST = SemistandardTableaux(3, [2,1]) sage: SST == loads(dumps(SST)) True """ self.n = n self.mu = mu | 460,750 |
def __contains__(self, x): """ TESTS:: sage: SST = SemistandardTableaux(6, [2,2,2]) sage: all([sst in SST for sst in SST]) True sage: all([sst in SST for sst in SemistandardTableaux([3,2,1],[2,2,2])]) True """ return x in SemistandardTableaux_all() and x in SemistandardTableaux(map(len, x), self.mu) | def __contains__(self, x): """ TESTS:: sage: SST = SemistandardTableaux(6, [2,2,2]) sage: all([sst in SST for sst in SST]) True sage: all([sst in SST for sst in SemistandardTableaux([3,2,1],[2,2,2])]) True """ return x in SemistandardTableaux_all() and x in SemistandardTableaux(map(len, x), self.mu) | 460,751 |
def is_planar(self, on_embedding=None, kuratowski=False, set_embedding=False, set_pos=False): """ Returns True if the graph is planar, and False otherwise. This wraps the reference implementation provided by John Boyer of the linear time planarity algorithm by edge addition due to Boyer Myrvold. (See reference code in ... | def is_planar(self, on_embedding=None, kuratowski=False, set_embedding=False, set_pos=False): Multi-edged and looped graphs are partially supported:: sage: G = Graph({0:[1,1]}, multiedges=True) sage: G.is_planar() True sage: G.is_planar(on_embedding={}) Traceback (most recent call last): ... NotImplementedError: Cann... | 460,752 |
def RealProjectiveSpace(self, n): r""" A triangulation of `\Bold{R}P^n` for any `n \geq 0`. | def RealProjectiveSpace(self, n): r""" A triangulation of `\Bold{R}P^n` for any `n \geq 0`. | 460,753 |
def RealProjectiveSpace(self, n): r""" A triangulation of `\Bold{R}P^n` for any `n \geq 0`. | def RealProjectiveSpace(self, n): r""" A triangulation of `\Bold{R}P^n` for any `n \geq 0`. | 460,754 |
def RealProjectiveSpace(self, n): r""" A triangulation of `\Bold{R}P^n` for any `n \geq 0`. | def RealProjectiveSpace(self, n): r""" A triangulation of `\Bold{R}P^n` for any `n \geq 0`. | 460,755 |
def RealProjectiveSpace(self, n): r""" A triangulation of `\Bold{R}P^n` for any `n \geq 0`. | def RealProjectiveSpace(self, n): r""" A triangulation of `\Bold{R}P^n` for any `n \geq 0`. | 460,756 |
def _compute_faces(self): r""" Compute and cache faces of this polytope. If this polytope is reflexive and the polar polytope was already computed, computes faces of both in order to save time and preserve the one-to-one correspondence between the faces of this polytope of dimension d and the faces of the polar polyto... | def _compute_faces(self): r""" Compute and cache faces of this polytope. If this polytope is reflexive and the polar polytope was already computed, computes faces of both in order to save time and preserve the one-to-one correspondence between the faces of this polytope of dimension d and the faces of the polar polyto... | 460,757 |
def faces(self, dim=None, codim=None): r""" Return the sequence of faces of this polytope. If ``dim`` or ``codim`` are specified, returns a sequence of faces of the corresponding dimension or codimension. Otherwise returns the sequence of such sequences for all dimensions. EXAMPLES: All faces of the 3-dimensional oct... | def faces(self, dim=None, codim=None): r""" Return the sequence of proper faces of this polytope. If ``dim`` or ``codim`` are specified, returns a sequence of faces of the corresponding dimension or codimension. Otherwise returns the sequence of such sequences for all dimensions. EXAMPLES: All faces of the 3-dimensio... | 460,758 |
def points(self): r""" Return all lattice points of this polytope as columns of a matrix. EXAMPLES: The lattice points of the 3-dimensional octahedron and its polar cube:: sage: o = lattice_polytope.octahedron(3) sage: o.points() [ 1 0 0 -1 0 0 0] [ 0 1 0 0 -1 0 0] [ 0 0 1 0 0 -1 0] sage: cube = o.pola... | def points(self): r""" Return all lattice points of this polytope as columns of a matrix. EXAMPLES: The lattice points of the 3-dimensional octahedron and its polar cube:: sage: o = lattice_polytope.octahedron(3) sage: o.points() [ 1 0 0 -1 0 0 0] [ 0 1 0 0 -1 0 0] [ 0 0 1 0 0 -1 0] sage: cube = o.pola... | 460,759 |
def reduced_rauzy_graph(self, n): r""" Returns the reduced Rauzy graph of order `n` of self. | def reduced_rauzy_graph(self, n): r""" Returns the reduced Rauzy graph of order `n` of self. | 460,760 |
def reduced_rauzy_graph(self, n): r""" Returns the reduced Rauzy graph of order `n` of self. | def reduced_rauzy_graph(self, n): r""" Returns the reduced Rauzy graph of order `n` of self. | 460,761 |
def reduced_rauzy_graph(self, n): r""" Returns the reduced Rauzy graph of order `n` of self. | def reduced_rauzy_graph(self, n): r""" Returns the reduced Rauzy graph of order `n` of self. | 460,762 |
def reduced_rauzy_graph(self, n): r""" Returns the reduced Rauzy graph of order `n` of self. | def reduced_rauzy_graph(self, n): r""" Returns the reduced Rauzy graph of order `n` of self. | 460,763 |
def reduced_rauzy_graph(self, n): r""" Returns the reduced Rauzy graph of order `n` of self. | def reduced_rauzy_graph(self, n): r""" Returns the reduced Rauzy graph of order `n` of self. | 460,764 |
def reduced_rauzy_graph(self, n): r""" Returns the reduced Rauzy graph of order `n` of self. | def reduced_rauzy_graph(self, n): r""" Returns the reduced Rauzy graph of order `n` of self. | 460,765 |
def reduced_rauzy_graph(self, n): r""" Returns the reduced Rauzy graph of order `n` of self. | def reduced_rauzy_graph(self, n): r""" Returns the reduced Rauzy graph of order `n` of self. | 460,766 |
def reduced_rauzy_graph(self, n): r""" Returns the reduced Rauzy graph of order `n` of self. | def reduced_rauzy_graph(self, n): r""" Returns the reduced Rauzy graph of order `n` of self. | 460,767 |
def __init__(self, x, y, r1, r2, angle, options): """ Initializes base class Ellipse. | def __init__(self, x, y, r1, r2, angle, options): """ Initializes base class Ellipse. | 460,768 |
def get_minmax_data(self): """ Returns a dictionary with the bounding box data. | def get_minmax_data(self): """ Returns a dictionary with the bounding box data. | 460,769 |
def get_minmax_data(self): """ Returns a dictionary with the bounding box data. | def get_minmax_data(self): """ Returns a dictionary with the bounding box data. | 460,770 |
def get_minmax_data(self): """ Returns a dictionary with the bounding box data. | def get_minmax_data(self): """ Returns a dictionary with the bounding box data. | 460,771 |
def _allowed_options(self): """ Return the allowed options for the Ellipse class. | def _allowed_options(self): """ Return the allowed options for the Ellipse class. | 460,772 |
def _repr_(self): """ String representation of Ellipse primitive. | def _repr_(self): """ String representation of Ellipse primitive. | 460,773 |
def plot3d(self): r""" Plot 3d is not implemented. | def plot3d(self): r""" Plot 3d is not implemented. | 460,774 |
def __init__(self, parent, value, check=True): """ Create element of a finite field. EXAMPLES:: sage: from sage.rings.finite_rings.finite_field_ext_pari import FiniteField_ext_pari sage: k = FiniteField_ext_pari(9,'a') sage: a = k(11); a 2 sage: a.parent() Finite Field in a of size 3^2 sage: V = k.vector_space(); v =... | def __init__(self, parent, value, check=True): """ Create element of a finite field. EXAMPLES:: sage: from sage.rings.finite_rings.finite_field_ext_pari import FiniteField_ext_pari sage: k = FiniteField_ext_pari(9,'a') sage: a = k(11); a 2 sage: a.parent() Finite Field in a of size 3^2 sage: V = k.vector_space(); v =... | 460,775 |
def plot(self, *args, **kwds): """ Plot the real points of an affine patch of this projective plane curve. | def plot(self, *args, **kwds): """ Plot the real points of an affine patch of this projective plane curve. | 460,776 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points_iterator(self): r""" Return the rational points on this curve computed via enumeration. | 460,777 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | 460,778 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | 460,779 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | 460,780 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | 460,781 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | 460,782 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | 460,783 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | 460,784 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | 460,785 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | defrational_points(self,algorithm="enum",sort=True):r"""Returntherationalpointsonthiscurvecomputedviaenumeration. | 460,786 |
'@square...def g(x)...' | '@square...def g(x)...' | 460,787 |
def _sage_(self, R=None): """ Coerces self to Sage. EXAMPLES:: sage: R = singular.ring(0, '(x,y,z)', 'dp') sage: A = singular.matrix(2,2) sage: A._sage_(ZZ) [0 0] [0 0] sage: A = random_matrix(ZZ,3,3); A [ -8 2 1] [ -1 2 1] [-95 -1 -2] sage: As = singular(A); As -8 2 1 -1 2 1 -95 -1 -2... | def _sage_(self, R=None): """ Coerces self to Sage. EXAMPLES:: sage: R = singular.ring(0, '(x,y,z)', 'dp') sage: A = singular.matrix(2,2) sage: A._sage_(ZZ) [0 0] [0 0] sage: A = random_matrix(ZZ,3,3); A [ -8 2 1] [ -1 2 1] [-95 -1 -2] sage: As = singular(A); As -8 2 1 -1 2 1 -95 -1 -2 ... | 460,788 |
def search_doc(string, extra1='', extra2='', extra3='', extra4='', extra5='', **kwds): """ Search Sage HTML documentation for lines containing ``string``. The search is case-sensitive. The file paths in the output are relative to ``$SAGE_ROOT/devel/sage/doc/output``. INPUT: same as for :func:`search_src`. OUTPUT: sa... | def search_doc(string, extra1='', extra2='', extra3='', extra4='', extra5='', **kwds): """ Search Sage HTML documentation for lines containing ``string``. The search is case-sensitive. The file paths in the output are relative to ``$SAGE_ROOT/devel/sage/doc/output``. INPUT: same as for :func:`search_src`. OUTPUT: sa... | 460,789 |
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. | 460,790 |
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. | 460,791 |
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. | 460,792 |
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. | 460,793 |
def contour_plot(f, xrange, yrange, **options): r""" ``contour_plot`` takes a function of two variables, `f(x,y)` and plots contour lines of the function over the specified ``xrange`` and ``yrange`` as demonstrated below. ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)`` INPUT: - ``f`` -- a function of two variab... | def contour_plot(f, xrange, yrange, **options): r""" ``contour_plot`` takes a function of two variables, `f(x,y)` and plots contour lines of the function over the specified ``xrange`` and ``yrange`` as demonstrated below. ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)`` INPUT: - ``f`` -- a function of two variab... | 460,794 |
def contour_plot(f, xrange, yrange, **options): r""" ``contour_plot`` takes a function of two variables, `f(x,y)` and plots contour lines of the function over the specified ``xrange`` and ``yrange`` as demonstrated below. ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)`` INPUT: - ``f`` -- a function of two variab... | def contour_plot(f, xrange, yrange, **options): r""" ``contour_plot`` takes a function of two variables, `f(x,y)` and plots contour lines of the function over the specified ``xrange`` and ``yrange`` as demonstrated below. ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)`` INPUT: - ``f`` -- a function of two variab... | 460,795 |
def contour_plot(f, xrange, yrange, **options): r""" ``contour_plot`` takes a function of two variables, `f(x,y)` and plots contour lines of the function over the specified ``xrange`` and ``yrange`` as demonstrated below. ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)`` INPUT: - ``f`` -- a function of two variab... | def contour_plot(f, xrange, yrange, **options): r""" ``contour_plot`` takes a function of two variables, `f(x,y)` and plots contour lines of the function over the specified ``xrange`` and ``yrange`` as demonstrated below. ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)`` INPUT: - ``f`` -- a function of two variab... | 460,796 |
... def __repr__(self): | ... def __repr__(self): | 460,797 |
... def __repr__(self): | ... def __repr__(self): | 460,798 |
... def __repr__(self): | ... def __repr__(self): | 460,799 |
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