_fmpz_mod_poly_discriminant, fmpz_mod_poly_discriminant
Synopsis
#include <flint/fmpz_mod_poly.h>void _fmpz_mod_poly_discriminant(fmpz_t d, const fmpz * poly, slong len, const fmpz_mod_ctx_t ctx)sourcevoid fmpz_mod_poly_discriminant(fmpz_t d, const fmpz_mod_poly_t f, const fmpz_mod_ctx_t ctx)sourceSet d to the discriminant of f, normalised as
\operatorname{disc}(f) = (-1)^{n(n-1)/2}\, \operatorname{res}(f, f') \,
\operatorname{lc}(f)^{-(n - m)}
with n = \deg f and m = \deg f' (so \operatorname{lc}(f)^{-1} when p \nmid n); then \operatorname{disc}(f) = \operatorname{lc}(f)^{2n-2} \prod_{i < j} (r_i - r_j)^2 over the roots r_i of f. The discriminant of a polynomial of degree less than 1, or with f' = 0, is zero. The underscore version requires \mathit{len} > 1.
Cite this page
The FLINT team, “_fmpz_mod_poly_discriminant, fmpz_mod_poly_discriminant (fmpz_mod_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpz_mod_poly/_fmpz_mod_poly_discriminant.html (generated 2026-10-20).
@misc{flint-doc-fmpz-mod-poly-fmpz-mod-poly-discriminant,
author = {{The FLINT team}},
title = {{\_fmpz\_mod\_poly\_discriminant, fmpz\_mod\_poly\_discriminant (fmpz\_mod\_poly.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/fmpz_mod_poly/_fmpz_mod_poly_discriminant.html},
note = {Generated 2026-10-20}
}