`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#

Elementary functions

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 2026-11-02).

@misc{flint-doc-arb-arb-pow,
  author       = {{The FLINT team}},
  title        = {{arb\_pow (arb.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/arb/arb_pow.html},
  note         = {Generated 2026-11-02}
}

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