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Package sage :: Package modular :: Package modsym :: Module manin_symbols :: Class ManinSymbol |
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Method Summary | |
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The Manin symbol [X^i*Y^(k-2-i),(u,v)] where k is the weight. | |
__cmp__(self,
other)
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__mul__(self,
matrix)
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__repr__(self)
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Return the image of self under the matrix [a,b;c,d]. | |
copy(self)
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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)
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Method Details |
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__init__(self,
parent,
i=0,
u=1,
v=1)
The Manin symbol [X^i*Y^(k-2-i),(u,v)] where k is the weight.
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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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