ca_is_cyclotomic_nf_elem
Synopsis
#include <flint/ca.h>Returns whether x is represented as an element of a field \mathbb{Q}(a) whose generator a is a root of unity. In that case, if p and q are not NULL, sets them to the integers with 0 \le p < q and \gcd(p, q) = 1 such that a = e^{2 \pi i p / q}.
Elements of \mathbb{Q} do not count: the result is 0 for a rational representation. The answer 0 does not prove that x lies in no cyclotomic field, and q need not be the conductor of the smallest cyclotomic field containing x.
Cite this page
The FLINT team, “ca_is_cyclotomic_nf_elem (ca.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/ca/ca_is_cyclotomic_nf_elem.html (generated 2026-10-20).
@misc{flint-doc-ca-ca-is-cyclotomic-nf-elem,
author = {{The FLINT team}},
title = {{ca\_is\_cyclotomic\_nf\_elem (ca.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/ca/ca_is_cyclotomic_nf_elem.html},
note = {Generated 2026-10-20}
}