fmpz_poly_factor_mignotte
Synopsis
#include <flint/fmpz_poly_factor.h>void fmpz_poly_factor_mignotte(fmpz_t B, const fmpz_poly_t f)sourceSets B to a bound for the absolute values of the coefficients of all factors in \mathbb{Z}[x] of f of degree m \ge 2: the maximum of |f(0)|, |\operatorname{lc}(f)| and of \binom{m-1}{j} N + \binom{m-1}{j-1} |\operatorname{lc}(f)| for 1 \le j < m, where N \ge \|f\|_2 is an integer [Coh1996, Theorem 3.5.1]. The Zassenhaus algorithm lifts to p^a > 2 |\operatorname{lc}(f)| B.
References#
- [Coh1996] Cohen, Henri : A course in computational algebraic number theory, Springer, 1996
Cite this page
The FLINT team, “fmpz_poly_factor_mignotte (fmpz_poly_factor.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpz_poly_factor/fmpz_poly_factor_mignotte.html (generated 2026-10-20).
@misc{flint-doc-fmpz-poly-factor-fmpz-poly-factor-mignotte,
author = {{The FLINT team}},
title = {{fmpz\_poly\_factor\_mignotte (fmpz\_poly\_factor.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/fmpz_poly_factor/fmpz_poly_factor_mignotte.html},
note = {Generated 2026-10-20}
}