FLINT3.7.0-dev
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fmpq_poly_resultant

Synopsis#include <flint/fmpq_poly.h>
void fmpq_poly_resultant(fmpq_t r, const fmpq_poly_t f, const fmpq_poly_t g)source

Returns the resultant of ff and gg.

Enumerating the roots of ff and gg over Qˉ\bar{\mathbf{Q}} as r1,…,rmr_1, \dotsc, r_m and s1,…,sns_1, \dotsc, s_n, respectively, and letting xx and yy denote the leading coefficients, the resultant is defined as

xnym∏i=1m∏j=1n(ri−sj).x^{n} y^{m} \prod_{i=1}^{m} \prod_{j=1}^{n} (r_i - s_j).

We handle special cases as follows: if one of the polynomials is zero, the resultant is zero. Otherwise, if one of the polynomials is constant, the last term in the above expression is the empty product.

Cite this page

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