`fmpz_mpoly_factor_bound_si`

Synopsis#include <flint/fmpz_mpoly_factor.h>

int fmpz_mpoly_factor_bound_si(fmpz_t B, const fmpz_t A, const slong * degs, slong nvars)source

Sets $B$ to a bound on the coefficients of the divisors of a polynomial $f$ whose coefficients are bounded by $A$ in absolute value and whose degrees in its $n$ = nvars variables are $d_0, \ldots, d_{n-1}$ (degs): $B = |A| \cdot (\lfloor \sqrt{\lceil \prod_i (d_i + 1) / 2^{n} \rceil} \rfloor + 1) \cdot 2^{\sum_i d_i}$ , and $B = 0$ if some $d_i < 0$ . Returns 0 if the degree sum overflows and 1 otherwise. fmpz_mpolyl_gcd_zippel uses this bound to decide when to give up on a modular reconstruction and start over.

Cite this page

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

@misc{flint-doc-fmpz-mpoly-factor-fmpz-mpoly-factor-bound-si,
  author       = {{The FLINT team}},
  title        = {{fmpz\_mpoly\_factor\_bound\_si (fmpz\_mpoly\_factor.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/fmpz_mpoly_factor/fmpz_mpoly_factor_bound_si.html},
  note         = {Generated 2026-11-02}
}

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