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Package sage :: Package modular :: Package modsym :: Module manin_symbols |
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Classes | |
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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 | |
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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 |
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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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