_arb_poly_newton_convergence_factor
Synopsis
#include <flint/arb_poly.h>void _arb_poly_newton_convergence_factor(arf_t convergence_factor, arb_srcptr poly, slong len, const arb_t convergence_interval, slong prec)sourceSets convergence_factor to an upper bound for C = \sup_{t, u \in I} \tfrac12 |f''(t)| / |f'(u)|, where I is convergence_interval and f is {poly, len}, obtained by evaluating f' and f'' on I. The bound is infinite unless f' is bounded away from zero on I; for polynomials with large coefficients, I must be narrow.
Cite this page
The FLINT team, “_arb_poly_newton_convergence_factor (arb_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb_poly/_arb_poly_newton_convergence_factor.html (generated 2026-10-20).
@misc{flint-doc-arb-poly-arb-poly-newton-convergence-factor,
author = {{The FLINT team}},
title = {{\_arb\_poly\_newton\_convergence\_factor (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_newton_convergence_factor.html},
note = {Generated 2026-10-20}
}