ManinSymbolList_character(character, weight): INPUT: character - a dirichlet character weight - integer weight >= 2
sage: eps = DirichletGroup(4).gen(0) sage: m = ManinSymbolList_character(eps,2); m Manin Symbol List of weight 2 for Gamma1(4) with character [-1] sage: m.manin_symbol_list() [(0,1), (1,0), (1,1), (1,2), (1,3), (2,1)]
character, weight) |
apply,
apply_I,
apply_S,
apply_T,
apply_TT,
character,
index,
level,
normalize
Further documentation:
j, m) |
Apply the matrix m=[a,b,c,d] to the j-th Manin symbol.
INPUT: j -- integer m = [a, b, c, d] a list of 4 integers. OUTPUT: a list of pairs (j, alpha_i), where each alpha_i is an integer, j is an integer (the j-th Manin symbol), and the sum alpha_i*x_i is the image of self under the right action of the matrix [a,b;c,d]. Here the right action of g=[a,b;c,d] on a Manin symbol [P(X,Y),(u,v)] is [P(aX+bY,cX+dY),(u,v)*g].
sage: from sage.modular.dirichlet import * sage: eps = DirichletGroup(4).gen(0) sage: m = ManinSymbolList_character(eps,4) sage: m[6] (1, 0, 1) sage: m.apply(4, [1,0,0,1]) [(4, 1)] sage: m.apply(1, [-1,0,0,1]) [(1, -1)]
x) |
Compute the index into the list of standard Manin symbols of a symbol that is equivalent, modulo a scalar s, to x. Returns the index and the scalar.
If x is not in the list, then this function returns -1, 0.
INPUT: x -- 3-tuple of ints. Something equivalent to an element of Manin symbols list, which need not be normalized. OUTPUT: int -- the index of the Manin symbol equivalent to (i,u,v). scalar -- element of the base field or the int 0.
Instances of class ManinSymbolList_character also have the following special methods:
__repr__
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