List of coset representatives for \(\Gamma_H(N)\) in \({\rm SL}_2(\ZZ)\)¶
- class sage.modular.modsym.ghlist.GHlist(group)¶
Bases:
sage.structure.sage_object.SageObjectA class representing a list of coset representatives for \(\Gamma_H(N)\) in \({\rm SL}_2(\ZZ)\).
- list()¶
Return a list of vectors representing the cosets. Do not change the returned list!
EXAMPLES:
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)