FLINT3.7.0-dev
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acb_rsqrt, acb_rsqrt_analytic

Synopsis#include <flint/acb.h>
void acb_rsqrt(acb_t y, const acb_t x, slong prec)source
void acb_rsqrt_analytic(acb_t res, const acb_t z, int analytic, slong prec)source

Set the output to the principal reciprocal square root 1/z1/\sqrt{z}. analytic is as for acb_sqrt_analytic.

If one part is zero, a single real reciprocal square root suffices. In general 1/a+bi=((a+r)−bi)/v1/\sqrt{a + bi} = ((a + r) - bi)/v with r=∣a+bi∣r = |a + bi| and v=r∣a+bi+r∣2v = \sqrt{r |a + bi + r|^2}, which needs one real square root and one real reciprocal square root.

Guides#

Cite this page

The FLINT team, “acb_rsqrt, acb_rsqrt_analytic (acb.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb/acb_rsqrt.html (generated 2026-11-02).