List of coset representatives for in .

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

A class representing a list of coset representatives for in . What we actually calculate is a list of elements of of exact order .

TESTS:

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

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 of integers, return the unique pair such that the pair appears in self.list() and is equivalent to . This is rather trivial, but is here for consistency with the P1List class which is the equivalent for (where the problem is rather harder).

This will only make sense if ; 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)