A class representing a list of coset representatives for in
.
TESTS:
sage: L = sage.modular.modsym.ghlist.GHlist(GammaH(18,[13]))
sage: loads(dumps(L)) == L
True
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
EXAMPLE:
sage: L = sage.modular.modsym.ghlist.GHlist(GammaH(8, [5])); L[5] # indirect doctest
(1, 3)
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]
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
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 []'
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)]
Given a pair of integers, return the unique pair
such that the pair
appears in self.list() and
is equivalent to
.
This will only make sense if ; 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)