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

class sage.modular.modsym.g1list.G1list(N)

A class representing a list of coset representatives for \Gamma_1(N) in {\rm SL}_2(\ZZ). What we actually calculate is a list of elements of (\ZZ/N\ZZ)^2 of exact order N.

TESTS:

sage: L = sage.modular.modsym.g1list.G1list(18)
sage: loads(dumps(L)) == L
True
__cmp__(other)

Compare self to other.

EXAMPLE:

sage: L1 = sage.modular.modsym.g1list.G1list(6)
sage: L2 = sage.modular.modsym.g1list.G1list(7)
sage: L1 < L2
True
sage: L1 == QQ
False
__getitem__(i)

EXAMPLE:

sage: L = sage.modular.modsym.g1list.G1list(19); L[100] # indirect doctest
(5, 6)
__init__(N)

EXAMPLE:

sage: L = sage.modular.modsym.g1list.G1list(6); L # indirect doctest
List of coset representatives for Gamma_1(6) in SL_2(Z)
__len__()

Return the length of the underlying list.

EXAMPLE:

sage: L = sage.modular.modsym.g1list.G1list(24); len(L) # indirect doctest
384
__repr__()

String representation of self.

EXAMPLE:

sage: L = sage.modular.modsym.g1list.G1list(3); L.__repr__()
'List of coset representatives for Gamma_1(3) in SL_2(Z)'
list()

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

EXAMPLE:

sage: L = sage.modular.modsym.g1list.G1list(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 is rather trivial, but is here for consistency with the P1List class which is the equivalent for \Gamma_0 (where the problem is rather harder).

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

EXAMPLE:

sage: L = sage.modular.modsym.g1list.G1list(4); L.normalize(6, 1)
(2, 1)
sage: L = sage.modular.modsym.g1list.G1list(4); L.normalize(6, 2) # nonsense!
(2, 2)

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

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