List of coset representatives for \(\Gamma_H(N)\) in \(\SL_2(\ZZ)\)¶
- class sage.modular.modsym.ghlist.GHlist(group)[source]¶
- Bases: - SageObject- A class representing a list of coset representatives for \(\Gamma_H(N)\) in \(\SL_2(\ZZ)\). - list()[source]¶
- 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)] - >>> from sage.all import * >>> L = sage.modular.modsym.ghlist.GHlist(GammaH(Integer(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)[source]¶
- 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) - >>> from sage.all import * >>> sage.modular.modsym.ghlist.GHlist(GammaH(Integer(24), [Integer(17), Integer(19)])).normalize(Integer(17), Integer(6)) (1, 6) >>> sage.modular.modsym.ghlist.GHlist(GammaH(Integer(24), [Integer(7), Integer(13)])).normalize(Integer(17), Integer(6)) (5, 6) >>> sage.modular.modsym.ghlist.GHlist(GammaH(Integer(24), [Integer(5), Integer(23)])).normalize(Integer(17), Integer(6)) (7, 18)