8.6.2.3 ManinSymbolList_character Objects

class ManinSymbolList_character
List of Manin Symbols with character.

ManinSymbolList_character(character, weight): INPUT: character - a dirichlet character weight - integer weight >= 2 EXAMPLE:

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)]
ManinSymbolList_character( character, weight)

Instances of class ManinSymbolList_character have the following functions (in addition to inherited functions and special functions):

apply,$  $ apply_I,$  $ apply_S,$  $ apply_T,$  $ apply_TT,$  $ character,$  $ index,$  $ level,$  $ normalize

Further documentation:

apply( 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)]

apply_I( j)

apply_S( j)

index( 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.

See About this document... for information on suggesting changes.