List of coset representatives for \Gamma_H(N) in {\rm SL}_2(\ZZ).

class sage.modular.modsym.ghlist.GHlist(group)

A class representing a list of coset representatives for \Gamma_H(N) in {\rm SL}_2(\ZZ).

TESTS:

sage: L = sage.modular.modsym.ghlist.GHlist(GammaH(18,[13]))
sage: loads(dumps(L)) == L
True
__cmp__(other)

Compare self to other.

EXAMPLE:

sage: L1 = sage.modular.modsym.ghlist.GHlist(GammaH(18, [11]))
sage: L2 = sage.modular.modsym.ghlist.GHlist(GammaH(18, [13]))
sage: L1 < L2
True
sage: L1 == QQ
False
__getitem__(i)

EXAMPLE:

sage: L = sage.modular.modsym.ghlist.GHlist(GammaH(8, [5])); L[5] # indirect doctest
(1, 3)
__init__(group)

EXAMPLE:

sage: L = sage.modular.modsym.ghlist.GHlist(GammaH(8,[7])); L # indirect doctest
List of coset representatives for Congruence Subgroup Gamma_H(8) with H generated by [7]
__len__()

Return the length of the underlying list (the index of the group).

EXAMPLE:

sage: L = sage.modular.modsym.ghlist.GHlist(GammaH(24, [5])); len(L) # indirect doctest
192
__repr__()

String representation of self.

EXAMPLE:

sage: L = sage.modular.modsym.ghlist.GHlist(GammaH(3,[])); L.__repr__()
'List of coset representatives for Congruence Subgroup Gamma_H(3) with H generated by []'
list()

Return a list of vectors representing the cosets. Do not change the returned list!

EXAMPLE:

sage: L = sage.modular.modsym.ghlist.GHlist(GammaH(4,[])); L.list()
[(0, 1), (0, 3), (1, 0), (1, 1), (1, 2), (1, 3), (2, 1), (2, 3), (3, 0), (3, 1), (3, 2), (3, 3)]
normalize(u, v)

Given a pair (u,v) of integers, return the unique pair (u', v') such that the pair (u', v') appears in self.list() and (u, v) is equivalent to (u', v').

This will only make sense if {\rm gcd}(u, v, N) = 1; otherwise the output will not be an element of self.

EXAMPLES:

sage: sage.modular.modsym.ghlist.GHlist(GammaH(24, [17, 19])).normalize(17, 6)
(1, 6)
sage: sage.modular.modsym.ghlist.GHlist(GammaH(24, [7, 13])).normalize(17, 6)
(5, 6)
sage: sage.modular.modsym.ghlist.GHlist(GammaH(24, [5, 23])).normalize(17, 6)
(7, 18)

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List of coset representatives for \Gamma_1(N) in {\rm SL}_2(\ZZ).

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