FLINT3.7.0-dev
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arb_root_ui, arb_root

Synopsis#include <flint/arb.h>
void arb_root_ui(arb_t z, const arb_t x, ulong k, slong prec)source
void arb_root(arb_t z, const arb_t x, ulong k, slong prec)source

Set z to the principal k-th root of x. arb_root is an alias kept for compatibility.

For small k, the root of the midpoint is computed with arf_root and for x=[m±r]x = [m \pm r], r<mr < m, the propagated error is bounded by

m1/k−(m−r)1/k≤m1/kmin⁡(1,1klog⁡(1+rm−r)),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)\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 2026-11-02).