`nf_elem_coprime_den, nf_elem_coprime_den_signed`

Synopsis#include <flint/nf_elem.h>

void nf_elem_coprime_den(nf_elem_t res, const nf_elem_t a, const fmpz_t mod, const nf_t nf)source

void nf_elem_coprime_den_signed(nf_elem_t res, const nf_elem_t a, const fmpz_t mod, const nf_t nf)source

Set 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 2026-11-02).

@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 2026-11-02}
}

Edit this page · PDF version · Built with fdoc from 0a4634bf95