Monomial expansion of \((aX + bY)^i (cX + dY)^{j-i}\)¶
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class
sage.modular.modsym.apply.
Apply
¶ Bases:
object
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sage.modular.modsym.apply.
apply_to_monomial
(i, j, a, b, c, d)¶ Return a list of the coefficients of
\[(aX + bY)^i (cX + dY)^{j-i},\]where \(0 \leq i \leq j\), and \(a\), \(b\), \(c\), \(d\) are integers.
One should think of \(j\) as being \(k-2\) for the application to modular symbols.
INPUT:
i, j, a, b, c, d – all ints
OUTPUT:
list of ints, which are the coefficients of \(Y^j, Y^{j-1}X, \ldots, X^j\), respectively.
EXAMPLES:
We compute that \((X+Y)^2(X-Y) = X^3 + X^2Y - XY^2 - Y^3\):
sage: from sage.modular.modsym.apply import apply_to_monomial sage: apply_to_monomial(2, 3, 1,1,1,-1) [-1, -1, 1, 1] sage: apply_to_monomial(5, 8, 1,2,3,4) [2048, 9728, 20096, 23584, 17200, 7984, 2304, 378, 27] sage: apply_to_monomial(6,12, 1,1,1,-1) [1, 0, -6, 0, 15, 0, -20, 0, 15, 0, -6, 0, 1]