_arb_poly_swinnerton_dyer_ui, arb_poly_swinnerton_dyer_ui, _arb_poly_swinnerton_dyer_ui_prec
#include <flint/arb_poly.h>void arb_poly_swinnerton_dyer_ui(arb_poly_t poly, ulong n, slong prec)sourceSet poly to the Swinnerton-Dyer polynomial S_n = \prod (x \pm \sqrt{2} \pm \sqrt{3} \pm \cdots \pm \sqrt{p_n}) of degree 2^n, the minimal polynomial over \mathbb{Q} of the sum of the square roots of the first n primes. If prec is 0, the precision _arb_poly_swinnerton_dyer_ui_prec(n) is used, which is chosen so that arb_poly_get_unique_fmpz_poly should succeed.
The underscore version computes only the first trunc coefficients, but poly must have room for 2^n + 1 coefficients, which are used as temporary space. The factors are multiplied in a balanced tree of products of polynomials in x^2. The precision estimate is half of a bound derived from the binomial theorem, plus 15 bits; it is a heuristic. fmpz_poly_swinnerton_dyer uses these functions.
The FLINT team, “_arb_poly_swinnerton_dyer_ui, arb_poly_swinnerton_dyer_ui, _arb_poly_swinnerton_dyer_ui_prec (arb_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb_poly/_arb_poly_swinnerton_dyer_ui.html (generated 2026-10-20).
@misc{flint-doc-arb-poly-arb-poly-swinnerton-dyer-ui,
author = {{The FLINT team}},
title = {{\_arb\_poly\_swinnerton\_dyer\_ui, arb\_poly\_swinnerton\_dyer\_ui, \_arb\_poly\_swinnerton\_dyer\_ui\_prec (arb\_poly.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/arb_poly/_arb_poly_swinnerton_dyer_ui.html},
note = {Generated 2026-10-20}
}