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Python congroup_generic.CongruenceSubgroup类代码示例

本文整理汇总了Python中congroup_generic.CongruenceSubgroup的典型用法代码示例。如果您正苦于以下问题:Python CongruenceSubgroup类的具体用法?Python CongruenceSubgroup怎么用?Python CongruenceSubgroup使用的例子?那么, 这里精选的类代码示例或许可以为您提供帮助。


在下文中一共展示了CongruenceSubgroup类的6个代码示例,这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞,您的评价将有助于系统推荐出更棒的Python代码示例。

示例1: __init__

    def __init__(self, level):
        r"""
        The congruence subgroup `\Gamma_0(N)`.

        EXAMPLES::

            sage: G = Gamma0(11); G
            Congruence Subgroup Gamma0(11)
            sage: TestSuite(G).run()
            sage: G is loads(dumps(G))
            True

        TESTS::

            sage: g = Gamma0(5)([1,1,0,1])
            sage: g in Gamma0(7)
            True
            sage: g = Gamma0(5)([1,0,5,1])
            sage: g in Gamma0(7)
            False
            sage: g = Gamma0(2)([1,0,0,1])
            sage: g in SL2Z
            True
        """
        CongruenceSubgroup.__init__(self, level)
开发者ID:Findstat,项目名称:sage,代码行数:25,代码来源:congroup_gamma0.py

示例2: __cmp__

    def __cmp__(self, other):
        """
        Compare self to other.

        The ordering on congruence subgroups of the form GammaH(N) for
        some H is first by level and then by the subgroup H. In
        particular, this means that we have Gamma1(N) < GammaH(N) <
        Gamma0(N) for every nontrivial subgroup H.

        EXAMPLES::

            sage: G = GammaH(86, [9])
            sage: G.__cmp__(G)
            0
            sage: G.__cmp__(GammaH(86, [11])) is not 0
            True
            sage: Gamma1(11) < Gamma0(11)
            True
            sage: Gamma1(11) == GammaH(11, [])
            True
            sage: Gamma0(11) == GammaH(11, [2])
            True
        """
        if is_GammaH(other):
            t = cmp(self.level(), other.level())
            if t:
                return t
            else:
                return cmp(self._list_of_elements_in_H(), other._list_of_elements_in_H())
        else:
            return CongruenceSubgroup.__cmp__(self, other)
开发者ID:biasse,项目名称:sage,代码行数:31,代码来源:congroup_gammaH.py

示例3: __cmp__

    def __cmp__(self, other):
        """
        Compare self to other.

        The ordering on congruence subgroups of the form GammaH(N) for some H
        is first by level, then by the order of H, then lexicographically by H.
        In particular, this means that we have Gamma1(N) < GammaH(N) <
        Gamma0(N) for every nontrivial proper subgroup H.

        EXAMPLES::

            sage: G = GammaH(86, [9])
            sage: G.__cmp__(G)
            0
            sage: G.__cmp__(GammaH(86, [11])) is not 0
            True
            sage: Gamma1(11) < Gamma0(11)
            True
            sage: Gamma1(11) == GammaH(11, [])
            True
            sage: Gamma0(11) == GammaH(11, [2])
            True
            sage: G = Gamma0(86)
            sage: G.__cmp__(G)
            0
            sage: G.__cmp__(GammaH(86, [11])) is not 0
            True
            sage: Gamma1(17) < Gamma0(17)
            True
            sage: Gamma0(1) == SL2Z
            True
            sage: Gamma0(2) == Gamma1(2)
            True

            sage: [x._list_of_elements_in_H() for x in sorted(Gamma0(24).gamma_h_subgroups())]
            [[1],
            [1, 5],
            [1, 7],
            [1, 11],
            [1, 13],
            [1, 17],
            [1, 19],
            [1, 23],
            [1, 5, 7, 11],
            [1, 5, 13, 17],
            [1, 5, 19, 23],
            [1, 7, 13, 19],
            [1, 7, 17, 23],
            [1, 11, 13, 23],
            [1, 11, 17, 19],
            [1, 5, 7, 11, 13, 17, 19, 23]]
        """
        if is_GammaH(other):
            return (cmp(self.level(), other.level())
                or -cmp(self.index(), other.index())
                or cmp(self._list_of_elements_in_H(), other._list_of_elements_in_H()))
        else:
            return CongruenceSubgroup.__cmp__(self, other)
开发者ID:NitikaAgarwal,项目名称:sage,代码行数:58,代码来源:congroup_gammaH.py

示例4: __init__

    def __init__(self, level, H, Hlist=None):
        r"""
        The congruence subgroup `\Gamma_H(N)`. The subgroup H
        must be input as a list.

        EXAMPLES::

            sage: GammaH(117, [4])
            Congruence Subgroup Gamma_H(117) with H generated by [4]
            sage: G = GammaH(16, [7])
            sage: TestSuite(G).run()
            sage: G is loads(dumps(G))
            True
        """
        CongruenceSubgroup.__init__(self, level)
        self.__H = H
        if Hlist is None: Hlist = _list_subgroup(level, H)
        self.__Hlist = Hlist
开发者ID:NitikaAgarwal,项目名称:sage,代码行数:18,代码来源:congroup_gammaH.py

示例5: are_equivalent

    def are_equivalent(self, x, y, trans=False):
        r"""
        Check if the cusps `x` and `y` are equivalent under the action of this group.

        ALGORITHM: The cusps `u_1 / v_1` and `u_2 / v_2` are equivalent modulo
        `\Gamma(N)` if and only if `(u_1, v_1) = \pm (u_2, v_2) \bmod N`.
        
        EXAMPLE::

            sage: Gamma(7).are_equivalent(Cusp(2/3), Cusp(5/4))
            True
        """
        if trans:
            return CongruenceSubgroup.are_equivalent(self, x,y,trans=trans)
        N = self.level()
        u1,v1 = (x.numerator() % N, x.denominator() % N)
        u2,v2 = (y.numerator(), y.denominator())

        return ((u1,v1) == (u2 % N, v2 % N)) or ((u1,v1) == (-u2 % N, -v2 % N)) 
开发者ID:bgxcpku,项目名称:sagelib,代码行数:19,代码来源:congroup_gamma.py

示例6: __cmp__

    def __cmp__(self, other):
        r"""
        Compare self to other.

        EXAMPLES::

            sage: Gamma(3) == SymmetricGroup(8)
            False
            sage: Gamma(3) == Gamma1(3)
            False
            sage: Gamma(5) < Gamma(6)
            True
            sage: Gamma(5) == Gamma(5)
            True
            sage: Gamma(3) == Gamma(3).as_permutation_group()
            True
        """
        if is_Gamma(other):
            return cmp(self.level(), other.level())
        else:
            return CongruenceSubgroup.__cmp__(self, other)
开发者ID:Babyll,项目名称:sage,代码行数:21,代码来源:congroup_gamma.py


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