ca_sqrt_inert, ca_sqrt_nofactor, ca_sqrt_factor, ca_sqrt

The inert version returns the generator of the field $\mathbb{Q}(\sqrt{x})$ without trying to simplify. The nofactor version tries cheap simplifications, in particular an exact evaluation of $\sqrt{x}$ as an algebraic number of moderate degree. The factor version also writes $x = A^2 B$ by factoring the representation of $x$ (with the factorisation options flags, see ca_factor) and returns $\pm A \sqrt{B}$ with the sign chosen to give the principal root; the factorisation is a heuristic and $B$ need not be minimal. ca_sqrt currently calls ca_sqrt_factor with CA_FACTOR_POLY_SQF | CA_FACTOR_ZZ_SMOOTH, so that for example $\sqrt{12 \pi}$ becomes $2 \sqrt{3 \pi}$.

For special values: $\sqrt{c \infty} = \sqrt{c} \, \infty$, $\sqrt{\tilde \infty} = \tilde \infty$, and Undefined and Unknown map to themselves.

@misc{flint-doc-ca-ca-sqrt-inert,
  author       = {{The FLINT team}},
  title        = {{ca\_sqrt\_inert, ca\_sqrt\_nofactor, ca\_sqrt\_factor, ca\_sqrt (ca.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/ca/ca_sqrt_inert.html},
  note         = {Generated 2026-11-02}
}