Package sage :: Package modular :: Package modsym :: Module manin_symbols
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Module sage.modular.modsym.manin_symbols

Manin symbols
Classes
ManinSymbol A Manin symbol [X^i*Y^(k-2-i),(u,v)].
ManinSymbolList All sage symbols for a given group, weight, and character.
ManinSymbolList_character List of Manin Symbols with character.
ManinSymbolList_gamma0 List of Manin symbols for Gamma0(N).
ManinSymbolList_gamma1 List of Manin symbols for Gamma0(N).

Function Summary
  apply_to_monomial(i, j, a, b, c, d)
Returns a list of the coefficients of (a*X+b*Y)^i*(c*X+d*Y)^(j-i), where 0 <= i <= j, and a,b,c,d are integers.

Function Details

apply_to_monomial(i, j, a, b, c, d)

Returns a list of the coefficients of 
         (a*X+b*Y)^i*(c*X+d*Y)^(j-i),
where 0 <= i <= j, and a,b,c,d are integers.
INPUT:
    i, j, a, b, c, d -- all ints
OUTPUT:
    list of ints, which are the coefficients
    of Y^j, Y^(j-1)*X, ..., X^j, respectively.
EXAMPLE:
We compute (X+Y)^2*(X-Y)  (=X^3 + X^2*Y - X*Y^2 - Y^3)
    >>> apply_to_monomial(2, 3, 1,1,1,-1)
    [-1, -1, 1, 1]
    >>> apply_to_monomial(5, 8, 1,2,3,4)
    [2048, 9728, 20096, 23584, 17200, 7984, 2304, 378, 27]
    >>> apply_to_monomial(6,12, 1,1,1,-1)
    [1, 0, -6, 0, 15, 0, -20, 0, 15, 0, -6, 0, 1]

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