parent, t) |
Create a Manin symbol
, where
is
the weight.
INPUT: parent -- ManinSymbolList t -- a 3-tuple (i,u,v) of int's.
apply,
copy,
endpoints,
i,
lift_to_sl2z,
modular_symbol_rep,
parent,
tuple,
u,
v,
weight
Further documentation:
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].
[N=None]) |
Returns cusps alpha, beta such that this Manin symbol, viewed
as a symbol for level N, is
.
N) |
If this Manin symbol is (c,d) viewed modulo N, 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).
) |
Returns a representation of self as a formal sum of modular symbols. (The result is not cached.)
Instances of class ManinSymbol also have the following special functions:
__cmp__,
__mul__
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