`_fmpz_poly_swinnerton_dyer, fmpz_poly_swinnerton_dyer`

Synopsis#include <flint/fmpz_poly.h>

void _fmpz_poly_swinnerton_dyer(fmpz * T, ulong n)source

void fmpz_poly_swinnerton_dyer(fmpz_poly_t poly, ulong n)source

Set 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 2026-11-02).

@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 2026-11-02}
}

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