FLINT3.7.0-dev
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_fmpz_mod_poly_divrem, fmpz_mod_poly_divrem

Synopsis#include <flint/fmpz_mod_poly.h>
void _fmpz_mod_poly_divrem(fmpz * Q, fmpz * R, const fmpz * A, slong lenA, const fmpz * B, slong lenB, const fmpz_t invB, const fmpz_mod_ctx_t ctx)source
void fmpz_mod_poly_divrem(fmpz_mod_poly_t Q, fmpz_mod_poly_t R, const fmpz_mod_poly_t A, const fmpz_mod_poly_t B, const fmpz_mod_ctx_t ctx)source

Compute QQ and RR with A=BQ+RA = BQ + R and deg⁡R<deg⁡B\deg R < \deg B. The leading coefficient of BB must be invertible; invB is its inverse. The underscore version requires lenA≥lenB>0\mathit{lenA} \ge \mathit{lenB} > 0, writes lenA−lenB+1\mathit{lenA} - \mathit{lenB} + 1 coefficients of QQ and lenB−1\mathit{lenB} - 1 of RR, allows zero-padding of AA and no aliasing. A zero BB raises FLINT_DIVZERO (except modulo 1).

Small cases (lenB at most 30 or quotients of length at most 11) use the classical algorithm; larger ones use Newton iteration (_gr_poly_divrem_newton, see Division with remainder), in O(M(lenA))O(M(\mathit{lenA})) operations.

Cite this page

The FLINT team, “_fmpz_mod_poly_divrem, fmpz_mod_poly_divrem (fmpz_mod_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpz_mod_poly/_fmpz_mod_poly_divrem.html (generated 2026-11-02).