FLINT3.7.0-dev
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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)source

Sets bound to a ball containing

C(x,r)=12πr∮∣z−x∣=r∣f(z)∣ ∣dz∣=∫01∣f(x+re2πit)∣ dt,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 rr is radius, by a step sum over n=16,32,64,…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 2026-11-02).