nf_elem_coprime_den, nf_elem_coprime_den_signed
Synopsis
#include <flint/nf_elem.h>void nf_elem_coprime_den_signed(nf_elem_t res, const nf_elem_t a, const fmpz_t mod, const nf_t nf)sourceSet res to an element congruent to a modulo m whose denominator divides m^\infty: writing q = q_1 q_2 with q_1 composed of the primes dividing m and q_2 coprime to m, the numerator of a is multiplied by q_2^{-1} modulo m q_1, reduced into [0, m q_1) (or the symmetric range for the signed version) and divided by q_1. Then a - \mathtt{res} has denominator coprime to m and numerator coefficients divisible by m.
Cite this page
The FLINT team, “nf_elem_coprime_den, nf_elem_coprime_den_signed (nf_elem.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/nf_elem/nf_elem_coprime_den.html (generated 2026-10-20).
@misc{flint-doc-nf-elem-nf-elem-coprime-den,
author = {{The FLINT team}},
title = {{nf\_elem\_coprime\_den, nf\_elem\_coprime\_den\_signed (nf\_elem.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/nf_elem/nf_elem_coprime_den.html},
note = {Generated 2026-10-20}
}