FLINT3.7.0-dev
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_fmpz_poly_pseudo_divrem_cohen, fmpz_poly_pseudo_divrem_cohen, _fmpz_poly_pseudo_rem_cohen, fmpz_poly_pseudo_rem_cohen

Synopsis#include <flint/fmpz_poly.h>
void _fmpz_poly_pseudo_divrem_cohen(fmpz * Q, fmpz * R, const fmpz * A, slong lenA, const fmpz * B, slong lenB)source
void fmpz_poly_pseudo_divrem_cohen(fmpz_poly_t Q, fmpz_poly_t R, const fmpz_poly_t A, const fmpz_poly_t B)source
void _fmpz_poly_pseudo_rem_cohen(fmpz * R, const fmpz * A, slong lenA, const fmpz * B, slong lenB)source
void fmpz_poly_pseudo_rem_cohen(fmpz_poly_t R, const fmpz_poly_t A, const fmpz_poly_t B)source

Pseudo-division with the exponent fixed at d=max⁡(0,len⁡(A)−len⁡(B)+1)d = \max(0, \operatorname{len}(A) - \operatorname{len}(B) + 1), by Algorithm 3.1.2 of [Coh1996]: ℓdA=BQ+R\ell^d A = BQ + R with deg⁡R<deg⁡B\deg R < \deg B. This is the pseudo-remainder of the subresultant algorithm; it is quadratic and meant for short polynomials. The underscore versions require lenA≥lenB>0\mathit{lenA} \ge \mathit{lenB} > 0, room for lenA\mathit{lenA} coefficients in RR, and allow RR to be equal to AA; no other aliasing.

References#

  • [Coh1996] Cohen, Henri : A course in computational algebraic number theory, Springer, 1996
Cite this page

The FLINT team, “_fmpz_poly_pseudo_divrem_cohen, fmpz_poly_pseudo_divrem_cohen, _fmpz_poly_pseudo_rem_cohen, fmpz_poly_pseudo_rem_cohen (fmpz_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpz_poly/_fmpz_poly_pseudo_divrem_cohen.html (generated 2026-11-02).