_fmpz_poly_positive_root_upper_bound_2exp_local_max, _fmpz_poly_positive_root_upper_bound_2exp, fmpz_poly_positive_root_upper_bound_2exp
Synopsis
#include <flint/fmpz_poly.h>slong fmpz_poly_positive_root_upper_bound_2exp(const fmpz_poly_t pol)sourceReturn e such that 2^e is an upper bound (not necessarily strict) for the positive real roots of pol, computed with the local-max bound of Akritas, Strzeboński and Vigklas [ASV2008] as implemented in SLV by Tsigaridas; WORD_MIN is returned if the bound shows that there are no positive roots. The non-underscore version returns 0 for the zero polynomial and ignores roots at zero.
References#
- [ASV2008] A. G. Akritas, A. W. Strzeboński and P. S. Vigklas. Improving the performance of the continued fractions method using new bounds of positive roots. Nonlinear Analysis: Modelling and Control 13 (2008), 265–279.
Cite this page
The FLINT team, “_fmpz_poly_positive_root_upper_bound_2exp_local_max, _fmpz_poly_positive_root_upper_bound_2exp, fmpz_poly_positive_root_upper_bound_2exp (fmpz_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpz_poly/_fmpz_poly_positive_root_upper_bound_2exp_local_max.html (generated 2026-10-20).
@misc{flint-doc-fmpz-poly-fmpz-poly-positive-root-upper-bound-2exp-local-max,
author = {{The FLINT team}},
title = {{\_fmpz\_poly\_positive\_root\_upper\_bound\_2exp\_local\_max, \_fmpz\_poly\_positive\_root\_upper\_bound\_2exp, fmpz\_poly\_positive\_root\_upper\_bound\_2exp (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_positive_root_upper_bound_2exp_local_max.html},
note = {Generated 2026-10-20}
}