FLINT3.7.0-dev
/

arb_pow

Synopsis#include <flint/arb.h>
void arb_pow(arb_t z, const arb_t x, const arb_t y, slong prec)source

Sets z to x^y: by binary exponentiation if y is a small exact integer, as (x^{1/2})^{2y} if y is a small exact half-integer, and as \exp(y \log x) otherwise, with x^y = \pm(-x)^y for negative x and exact integer y.

x^0 = 1 for every x, and 0^y is 0 for positive y and indeterminate otherwise. For a ball x = [a \pm a] with a > 0, which contains 0, and nonnegative y, the result is the finite ball [u/2 \pm u/2] with u \ge (2a)^y rather than an indeterminate value. Otherwise a base containing nonpositive numbers gives an indeterminate result unless y is an exact integer.

Guides#

Cite this page

The FLINT team, “arb_pow (arb.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb/arb_pow.html (generated 2026-10-20).