Package sage :: Package modular :: Package modsym :: Module manin_symbols :: Class ManinSymbolList_character
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Class ManinSymbolList_character

ManinSymbolList --+
                  |
                 ManinSymbolList_character


List of Manin Symbols with character.

ManinSymbolList_character(character, weight):
INPUT:
    character -- a dirichlet character
    weight -- integer weight >= 2
EXAMPLE:
    >>> from sage.modular.dirichlet import *
    >>> eps = DirichletGroup(4).gen(0)
    >>> m = ManinSymbolList_character(eps,2); m
    Manin Symbol List of weight 2 for Gamma1(4) with character [-1]
    >>> m.list()
    [(0, 0, 1), (0, 1, 0), (0, 1, 1), (0, 1, 2), (0, 1, 3), (0, 2, 1)]

Method Summary
  __init__(self, character, weight)
  __repr__(self)
  apply(self, j, m)
Apply the matrix m=[a,b,c,d] to the j-th Manin symbol.
  apply_I(self, j)
  apply_S(self, j)
  apply_T(self, j)
  apply_TT(self, j)
  character(self)
  index(self, x)
Return the index into the list of Manin symbols of x.
  level(self)
  manin_symbol(self, i)
  normalize(self, x)
    Inherited from ManinSymbolList
  __getitem__(self, n)
  __len__(self)
  list(self)
  weight(self)

Method Details

apply(self, 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 sage 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].
EXAMPLES:
    >>> from sage.modular.dirichlet import *
    >>> eps = DirichletGroup(4).gen(0)
    >>> m = ManinSymbolList_character(eps,4)
    >>> m[6]
    (1, 0, 1)
    >>> m.apply(4, [1,0,0,1])
    [(4, 1)]
    >>> m.apply(1, [-1,0,0,1])
    [(1, -1)]
Overrides:
sage.modular.modsym.manin_symbols.ManinSymbolList.apply

index(self, x)

Return the index into the list of Manin symbols of x.
If x is not in the list, then this function returns -1.
INPUT:
    x -- element of sage symbols list, which need not
         be normalized
OUTPUT:
    int -- the index of the Manin symbol equivalent to (i,u,v).
Overrides:
sage.modular.modsym.manin_symbols.ManinSymbolList.index

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