ca_pow_fmpq, ca_pow_fmpz, ca_pow_ui, ca_pow_si, ca_pow

Integer powers of rational numbers and of number field elements are computed exactly unless the size of the result would exceed about CA_OPT_PREC_LIMIT bits; in generic fields, $x^n$ is expanded by repeated multiplication for $|n| \le$ CA_OPT_POW_LIMIT. Exponents $n/2$ are computed via ca_sqrt, and $(z^a)^b$ is simplified to $z^{ab}$ when this is valid. Otherwise the result is the generator of a new field $\mathbb{Q}(x^y)$, which requires that $x$ is proved nonzero unless $y$ is a positive rational number; if that fails, the result is Unknown.

For special bases and integer exponents $n$: $\tilde \infty^n$ is $\tilde \infty$, 0 or Undefined for $n > 0$, $n < 0$ and $n = 0$; $(c \infty)^n = c^n \infty$ for $n > 0$, 0 for $n < 0$ and Undefined for $n = 0$; $0^n = \tilde \infty$ for $n < 0$. Non-integer powers involving special values give Unknown.

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