FLINT3.7.0-dev
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fmpz_poly_factor_zassenhaus_recombination, fmpz_poly_factor_zassenhaus_recombination_with_prune

Synopsis#include <flint/fmpz_poly_factor.h>
void fmpz_poly_factor_zassenhaus_recombination(fmpz_poly_factor_t final_fac, const fmpz_poly_factor_t lifted_fac, const fmpz_poly_t F, const fmpz_t P, slong exp)source
void fmpz_poly_factor_zassenhaus_recombination_with_prune(fmpz_poly_factor_t final_fac, const fmpz_poly_factor_t lifted_fac, const fmpz_poly_t F, const fmpz_t P, slong exp, const zassenhaus_prune_t Z)source

Find the irreducible factors of the squarefree primitive FF from its monic factors lifted_fac modulo P=paP = p^a, where P>2∣lc⁡(F)∣BP > 2 |\operatorname{lc}(F)| B for the Mignotte bound BB, by trying subsets of the modular factors in order of increasing size: for each subset SS, the product lc⁡(F)∏i∈Sgi\operatorname{lc}(F) \prod_{i \in S} g_i is reduced into the symmetric range modulo PP, its primitive part is tested as a divisor of FF, and true factors are removed together with their modular factors. Each factor is appended to final_fac with multiplicity exp. The with_prune version skips subsets whose total degree is impossible according to Z.

Cite this page

The FLINT team, “fmpz_poly_factor_zassenhaus_recombination, fmpz_poly_factor_zassenhaus_recombination_with_prune (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_zassenhaus_recombination.html (generated 2026-11-02).