`_fmpz_mod_poly_split_rabin`

Synopsis#include <flint/fmpz_mod_poly.h>

void _fmpz_mod_poly_split_rabin(fmpz_mod_poly_t a, fmpz_mod_poly_t b, const fmpz_mod_poly_t f, const fmpz_t halfp, fmpz_mod_poly_t t, fmpz_mod_poly_t t2, flint_rand_t randstate, const fmpz_mod_ctx_t ctx)

source

Splits $f$ of degree at least 2, assumed to have $\deg f$ distinct nonzero roots in $\mathbb{F}_p$ , into two nontrivial factors $a$ and $b$ with $\deg a \ge \deg b$ , as $a = \gcd(f, (x + \delta)^{(p-1)/2} - 1)$ for random $\delta$ (degree 2 is solved directly with a square root). halfp must be $(p - 1)/2$ , and $t$ , $t_2$ are scratch polynomials.

Cite this page

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

@misc{flint-doc-fmpz-mod-poly-fmpz-mod-poly-split-rabin,
  author       = {{The FLINT team}},
  title        = {{\_fmpz\_mod\_poly\_split\_rabin (fmpz\_mod\_poly.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/fmpz_mod_poly/_fmpz_mod_poly_split_rabin.html},
  note         = {Generated 2026-11-02}
}

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