arb_root_ui, arb_root
Synopsis
#include <flint/arb.h>For small k, the root of the midpoint is computed with arf_root and for x = [m \pm r], r < m, the propagated error is bounded by
m^{1/k} - (m - r)^{1/k} \le m^{1/k} \min\left(1, \frac{1}{k}
\log\left(1 + \frac{r}{m - r}\right)\right),
evaluated with mag_log1p. For large k, the root is computed as \exp(\log(x)/k).
Cite this page
The FLINT team, “arb_root_ui, arb_root (arb.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb/arb_root_ui.html (generated 2026-10-20).
@misc{flint-doc-arb-arb-root-ui,
author = {{The FLINT team}},
title = {{arb\_root\_ui, arb\_root (arb.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/arb/arb_root_ui.html},
note = {Generated 2026-10-20}
}