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


A Manin symbol [X^i*Y^(k-2-i),(u,v)].
Method Summary
  __init__(self, parent, i, u, v)
The Manin symbol [X^i*Y^(k-2-i),(u,v)] where k is the weight.
  __cmp__(self, other)
  __mul__(self, matrix)
  __repr__(self)
  apply(self, a, b, c, d)
Return the image of self under the matrix [a,b;c,d].
  copy(self)
  lift_to_sl2z(self, level)
If this sage symbol is (c,d) viewed mod level, this function computes and returns a list [a,b, c',d'] that defines a 2x2 matrix with determinant 1 and integer entries, such that c=c'(mod N) and d=d'(mod N).
  weight(self)

Method Details

__init__(self, parent, i=0, u=1, v=1)
(Constructor)

The Manin symbol [X^i*Y^(k-2-i),(u,v)] where k is the weight.

apply(self, a, b, c, d)

Return the image of self under the matrix [a,b;c,d].
INPUT:
    a, b, c, d -- integers
OUTPUT:
    a list of pairs (alpha_i, x_i), where each alpha_i is an integer, 
    x_i is a 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].

lift_to_sl2z(self, level)

If this sage symbol is (c,d) viewed mod level, this function computes and returns a list [a,b, c',d'] that defines a 2x2 matrix with determinant 1 and integer entries, such that c=c'(mod N) and d=d'(mod N).

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