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)sourceReturns the resultant of f and g.
Enumerating the roots of f and g over \bar{\mathbf{Q}} as r_1, \dotsc, r_m and s_1, \dotsc, s_n, respectively, and letting x and y denote the leading coefficients, the resultant is defined as
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 2026-10-20).
@misc{flint-doc-fmpq-poly-fmpq-poly-resultant,
author = {{The FLINT team}},
title = {{fmpq\_poly\_resultant (fmpq\_poly.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/fmpq_poly/fmpq_poly_resultant.html},
note = {Generated 2026-10-20}
}