FLINT3.7.0-dev
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_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)source
void fmpz_mod_poly_discriminant(fmpz_t d, const fmpz_mod_poly_t f, const fmpz_mod_ctx_t ctx)source

Set dd to the discriminant of ff, normalised as

disc⁡(f)=(−1)n(n−1)/2 res⁡(f,f′) lc⁡(f)−(n−m)\operatorname{disc}(f) = (-1)^{n(n-1)/2}\, \operatorname{res}(f, f') \, \operatorname{lc}(f)^{-(n - m)}

with n=deg⁡fn = \deg f and m=deg⁡f′m = \deg f' (so lc⁡(f)−1\operatorname{lc}(f)^{-1} when p∤np \nmid n); then disc⁡(f)=lc⁡(f)2n−2∏i<j(ri−rj)2\operatorname{disc}(f) = \operatorname{lc}(f)^{2n-2} \prod_{i < j} (r_i - r_j)^2 over the roots rir_i of ff. The discriminant of a polynomial of degree less than 1, or with f′=0f' = 0, is zero. The underscore version requires len>1\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 2026-11-02).