Python Partition.size方法代码示例

# 需要导入模块: from sage.combinat.partition import Partition [as 别名]
# 或者: from sage.combinat.partition.Partition import size [as 别名]
    def __classcall_private__(cls, shape, weight):
        r"""
        Straighten arguments before unique representation.

        TESTS::

            sage: LR = LittlewoodRichardsonTableaux([3,2,1],[[2,1],[2,1]])
            sage: TestSuite(LR).run()
            sage: LittlewoodRichardsonTableaux([3,2,1],[[2,1]])
            Traceback (most recent call last):
            ...
            ValueError: the sizes of shapes and sequence of weights do not match
        """
        shape = Partition(shape)
        weight = tuple(Partition(a) for a in weight)
        if shape.size() != sum(a.size() for a in weight):
            raise ValueError("the sizes of shapes and sequence of weights do not match")
        return super(LittlewoodRichardsonTableaux, cls).__classcall__(cls, shape, weight)

# 需要导入模块: from sage.combinat.partition import Partition [as 别名]
# 或者: from sage.combinat.partition.Partition import size [as 别名]
    def __classcall_private__(cls, deg, par):
        r"""
        Create a primary similarity class type.

        EXAMPLES::

            sage: PrimarySimilarityClassType(2, [3, 2, 1])
            [2, [3, 2, 1]]

        The parent class is the class of primary similarity class types of order
        `d|\lambda\`::

            sage: PT = PrimarySimilarityClassType(2, [3, 2, 1])
            sage: PT.parent().size()
            12
        """
        par = Partition(par)
        P = PrimarySimilarityClassTypes(par.size() * deg)
        return P(deg, par)

# 需要导入模块: from sage.combinat.partition import Partition [as 别名]
# 或者: from sage.combinat.partition.Partition import size [as 别名]
    def coefficient_cycle_type(self, t):
        """
        Returns the coefficient of a cycle type ``t`` in ``self``.

        EXAMPLES::

            sage: from sage.combinat.species.generating_series import CycleIndexSeriesRing
            sage: p = SymmetricFunctions(QQ).power()
            sage: CIS = CycleIndexSeriesRing(QQ)
            sage: f = CIS([0, p([1]), 2*p([1,1]),3*p([2,1])])
            sage: f.coefficient_cycle_type([1])
            1
            sage: f.coefficient_cycle_type([1,1])
            2
            sage: f.coefficient_cycle_type([2,1])
            3
        """
        t = Partition(t)
        p = self.coefficient(t.size())
        return p.coefficient(t)

# 需要导入模块: from sage.combinat.partition import Partition [as 别名]
# 或者: from sage.combinat.partition.Partition import size [as 别名]

#.........这里部分代码省略.........
#                            return False
#                else:
#                    return True
#        else:
#            if 'representation_matrix' in other.__dict__:
#                return False
#            else:
#                return self.__dict__.__eq__(other.__dict__)

    def __call__(self, permutation):
        r"""
        Return the image of ``permutation`` in the representation.

        EXAMPLES::

            sage: spc = SymmetricGroupRepresentation([2,1])
            sage: spc([1,3,2])
            [ 1  0]
            [ 1 -1]
        """
        return self.representation_matrix(Permutation(permutation))

    def __iter__(self):
        r"""
        Iterate over the matrices representing the elements of the
        symmetric group.

        EXAMPLES::

            sage: spc = SymmetricGroupRepresentation([1,1,1])
            sage: list(spc)
            [[1], [-1], [-1], [1], [1], [-1]]
        """
        for permutation in Permutations(self._partition.size()):
            yield self.representation_matrix(permutation)

    def verify_representation(self):
        r"""
        Verify the representation: tests that the images of the simple
        transpositions are involutions and tests that the braid relations
        hold.

        EXAMPLES::

            sage: spc = SymmetricGroupRepresentation([1,1,1])
            sage: spc.verify_representation()
            True
            sage: spc = SymmetricGroupRepresentation([4,2,1])
            sage: spc.verify_representation()
            True
        """
        n = self._partition.size()
        transpositions = []
        for i in range(1,n):
            si = Permutation(range(1,i) + [i+1,i] + range(i+2,n+1))
            transpositions.append(si)
        repn_matrices = map(self.representation_matrix, transpositions)
        for (i,si) in enumerate(repn_matrices):
            for (j,sj) in enumerate(repn_matrices):
                if i == j:
                    if si*sj != si.parent().identity_matrix():
                        return False, "si si != 1 for i = %s" % (i,)
                elif abs(i-j) > 1:
                    if si*sj != sj*si:
                        return False, "si sj != sj si for (i,j) =(%s,%s)" % (i,j)
                else: