FLINT3.7.0-dev
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nmod_poly_is_irreducible

Synopsis#include <flint/nmod_poly_factor.h>
int nmod_poly_is_irreducible(const nmod_poly_t f)source

Returns whether f is irreducible over Fp\mathbb{F}_p. As a special case, constant polynomials, including zero, are considered irreducible (unlike gr_poly_is_irreducible, which returns false for them).

For p≤max⁡(200,2 len(f))p \le \max(200, 2\,\mathrm{len}(f)) the function first looks for a root by evaluating ff at every element of Fp\mathbb{F}_p. For degree below 600 it then uses nmod_poly_is_irreducible_ddf; for higher degrees it checks squarefreeness, looks for factors of degree at most 4 with gcd⁡(f,xpi−x)\gcd(f, x^{p^i} - x), and finishes with Rabin's test computed by modular composition (gr_poly_is_irreducible_rabin). See Irreducibility testing over finite fields.

Cite this page

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