_arb_poly_root_bound_fujiwara, arb_poly_root_bound_fujiwara
Synopsis
#include <flint/arb_poly.h>void _arb_poly_root_bound_fujiwara(mag_t bound, arb_srcptr poly, slong len)sourcevoid arb_poly_root_bound_fujiwara(mag_t bound, arb_poly_t poly)sourceSet bound to an upper bound for the absolute values of the complex roots of every polynomial in poly, using Fujiwara's bound [Fuj1916]
2 \max \left\{\left|\frac{a_{n-1}}{a_n}\right|,
\left|\frac{a_{n-2}}{a_n}\right|^{1/2}, \ldots,
\left|\frac{a_1}{a_n}\right|^{1/(n-1)},
\left|\frac{a_0}{2a_n}\right|^{1/n}\right\}.
The bound is infinite if the leading coefficient contains zero or the length is at most 1.
References#
- [Fuj1916] M. Fujiwara. Über die obere Schranke des absoluten Betrages der Wurzeln einer algebraischen Gleichung. Tôhoku Mathematical Journal 10 (1916), 167–171.
Cite this page
The FLINT team, “_arb_poly_root_bound_fujiwara, arb_poly_root_bound_fujiwara (arb_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb_poly/_arb_poly_root_bound_fujiwara.html (generated 2026-10-20).
@misc{flint-doc-arb-poly-arb-poly-root-bound-fujiwara,
author = {{The FLINT team}},
title = {{\_arb\_poly\_root\_bound\_fujiwara, arb\_poly\_root\_bound\_fujiwara (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_root_bound_fujiwara.html},
note = {Generated 2026-10-20}
}