`qqbar_pow`

Synopsis#include <flint/qqbar.h>

int qqbar_pow(qqbar_t res, const qqbar_t x, const qqbar_t y)source

General exponentiation: if $x^y$ is an algebraic number, sets res to it and returns 1; if $x^y$ is transcendental or undefined, returns 0. By the Gelfond–Schneider theorem, $x^y$ for algebraic $x \notin \{0, 1\}$ and irrational algebraic $y$ is transcendental, so the result is algebraic only if $y$ is rational, $x \in \{0, 1\}$ or $y = 0$ . Unlike the other functions, this one returns 0 instead of throwing for $0^y$ with $\operatorname{Re}(y) \le 0$ , $y \ne 0$ .

Guides#

Using qqbar

Cite this page

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

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

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