acb_calc_cauchy_bound
Synopsis
#include <flint/acb_calc.h>void acb_calc_cauchy_bound(arb_t bound, acb_calc_func_t func, void * param, const acb_t x, const arb_t radius, slong maxdepth, slong prec)sourceSets bound to a ball containing
C(x, r) = \frac{1}{2\pi r} \oint_{|z - x| = r} |f(z)|\, |dz| = \int_0^1 |f(x + r e^{2\pi i t})|\, dt,
where r is radius, by a step sum over n = 16, 32, 64, \ldots arcs of the circle (at most maxdepth doublings), stopping when the enclosure excludes zero. The whole circle is subdivided uniformly, without adaptivity.
Cite this page
The FLINT team, “acb_calc_cauchy_bound (acb_calc.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_calc/acb_calc_cauchy_bound.html (generated 2026-10-20).
@misc{flint-doc-acb-calc-acb-calc-cauchy-bound,
author = {{The FLINT team}},
title = {{acb\_calc\_cauchy\_bound (acb\_calc.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb_calc/acb_calc_cauchy_bound.html},
note = {Generated 2026-10-20}
}