FLINT3.7.0-dev
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acb_theta_g2_transvectant

Synopsis#include <flint/acb_theta.h>
void acb_theta_g2_transvectant(acb_poly_t res, const acb_poly_t g, const acb_poly_t h, slong m, slong n, slong k, int lead, slong prec)source

Sets res to the kk-th transvectant of the polynomials gg and hh, seen as binary forms of degrees mm and nn (higher coefficients are ignored), or to its leading coefficient (as a constant polynomial) if lead is nonzero.

With gg, hh homogeneous in x1,x2x_1, x_2,

(g,h)k=(m−k)!(n−k)!m!n!∑j=0k(−1)k−j(kj)∂kg∂x1k−j∂x2j∂kh∂x1j∂x2k−j.(g,h)_k = \frac{(m-k)!(n-k)!}{m!n!} \sum_{j=0}^{k} (-1)^{k-j} \binom{k}{j} \frac{\partial^k g}{\partial x_1^{k-j}\partial x_2^j} \frac{\partial^k h}{\partial x_1^{j}\partial x_2^{k-j}}.
Cite this page

The FLINT team, “acb_theta_g2_transvectant (acb_theta.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_theta/acb_theta_g2_transvectant.html (generated 2026-11-02).