_fmpz_poly_swinnerton_dyer, fmpz_poly_swinnerton_dyer
Synopsis
#include <flint/fmpz_poly.h>void fmpz_poly_swinnerton_dyer(fmpz_poly_t poly, ulong n)sourceSet poly to the Swinnerton-Dyer polynomial S_n = \prod (x \pm \sqrt{2} \pm \sqrt{3} \pm \sqrt{5} \pm \cdots \pm \sqrt{p_n}), where p_n is the n-th prime and all sign combinations are taken. It has degree 2^n and is irreducible over \mathbb{Z}, but splits into factors of degree at most 2 modulo every prime, which makes it the standard worst case for the Zassenhaus algorithm.
Cite this page
The FLINT team, “_fmpz_poly_swinnerton_dyer, fmpz_poly_swinnerton_dyer (fmpz_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpz_poly/_fmpz_poly_swinnerton_dyer.html (generated 2026-10-20).
@misc{flint-doc-fmpz-poly-fmpz-poly-swinnerton-dyer,
author = {{The FLINT team}},
title = {{\_fmpz\_poly\_swinnerton\_dyer, fmpz\_poly\_swinnerton\_dyer (fmpz\_poly.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/fmpz_poly/_fmpz_poly_swinnerton_dyer.html},
note = {Generated 2026-10-20}
}