FLINT3.7.0-dev
/

fmpz_poly_hensel_lift_tree_recursive

Synopsis#include <flint/fmpz_poly.h>
void fmpz_poly_hensel_lift_tree_recursive(slong * link, fmpz_poly_t * v, fmpz_poly_t * w, fmpz_poly_t f, slong j, slong inv, const fmpz_t p0, const fmpz_t p1)source

Lifts the subtree of the Hensel tree (link, v, w) rooted at the pair v[j], v[j + 1], whose product is ff, from modulus p0p_0 to P=p0p1P = p_0 p_1 with 1<p1≤p01 < p_1 \le p_0. The cofactors are lifted if inv is 1, and not lifted if it is 0 (for the last step); with −1-1 the cofactors are lifted from the previous precision (when a lift is restarted). ff may be aliased with an entry of v or w, but the entries of v and w must be distinct.

At each node the two halves of the lift are fused: since p1∣p0p_1 \mid p_0, the moduli g mod p1g \bmod p_1 and h mod p1h \bmod p_1 and their Newton preinverses serve all four divisions, and when p∤f(0)p \nmid f(0) the new second factor is computed as an exact quotient H=f/GH = f/G modulo PP instead of a second lift. The arithmetic runs in gr rings chosen by the size of the modulus (nmod, mpn_mod or fmpz_mod). Small nodes use fmpz_poly_hensel_lift.

Cite this page

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