`ca_is_cyclotomic_nf_elem`

Synopsis#include <flint/ca.h>

int ca_is_cyclotomic_nf_elem(slong * p, ulong * q, const ca_t x, ca_ctx_t ctx)source

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 2026-11-02).

@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 2026-11-02}
}

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