_nmod_poly_div_newton_n_preinv, nmod_poly_div_newton_n_preinv
#include <flint/nmod_poly.h>void _nmod_poly_div_newton_n_preinv(nn_ptr Q, nn_srcptr A, slong lenA, nn_srcptr B, slong lenB, nn_srcptr Binv, slong lenBinv, nmod_t mod)sourcevoid nmod_poly_div_newton_n_preinv(nmod_poly_t Q, const nmod_poly_t A, const nmod_poly_t B, const nmod_poly_t Binv)sourceSet Q to the quotient of A by B, given the power series inverse Binv of the reversal of B (see Computing modulo a fixed polynomial). The quotient is the reversal of \operatorname{rev}(A) \cdot \mathit{Binv} \bmod x^{\mathit{lenQ}}, so Binv must be correct modulo x^{\mathit{lenQ}}, \mathit{lenQ} = \mathit{lenA} - \mathit{lenB} + 1. The underscore version requires \mathit{lenA} \ge \mathit{lenB} \ge 1, does not read B, and does not allow Q to overlap Binv.
Binv is usually computed with nmod_poly_inv_series(Binv, rev(B), lenB), which is enough for \mathit{lenA} \le 2 \mathit{lenB} - 1. A shorter Binv is allowed if its missing coefficients are zero, as after normalisation.
Guides#
The FLINT team, “_nmod_poly_div_newton_n_preinv, nmod_poly_div_newton_n_preinv (nmod_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/nmod_poly/_nmod_poly_div_newton_n_preinv.html (generated 2026-10-20).
@misc{flint-doc-nmod-poly-nmod-poly-div-newton-n-preinv,
author = {{The FLINT team}},
title = {{\_nmod\_poly\_div\_newton\_n\_preinv, nmod\_poly\_div\_newton\_n\_preinv (nmod\_poly.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/nmod_poly/_nmod_poly_div_newton_n_preinv.html},
note = {Generated 2026-10-20}
}