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)
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)
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
