`fmpz_poly_factor_mignotte`

Synopsis#include <flint/fmpz_poly_factor.h>

void fmpz_poly_factor_mignotte(fmpz_t B, const fmpz_poly_t f)source

Sets $B$ 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 2026-11-02).

@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 2026-11-02}
}

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