nf_init
Synopsis
#include <flint/nf.h>void nf_init(nf_t nf, const fmpq_poly_t pol)sourceInitialises nf for the defining polynomial pol, which must have degree at least 1 (otherwise the function throws). The polynomial is not checked to be irreducible: with a reducible polynomial the arithmetic is that of the ring \mathbf{Q}[x]/(f), and the result of inverting a zero divisor is meaningless (_nf_elem_invertible_check tests for this).
The power sums are computed by the recurrence of Newton's identities for a non-monic polynomial [Coh1996, p. 163], with a common denominator that is a power of the leading coefficient.
Guides#
- Getting started with nf_elem (
nf_elem)
References#
- [Coh1996] Cohen, Henri : A course in computational algebraic number theory, Springer, 1996
Cite this page
The FLINT team, “nf_init (nf.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/nf/nf_init.html (generated 2026-10-20).
@misc{flint-doc-nf-nf-init,
author = {{The FLINT team}},
title = {{nf\_init (nf.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/nf/nf_init.html},
note = {Generated 2026-10-20}
}