Computing Generic Fibres of Polynomial Ideals with FGLM and Hensel Lifting

Jérémy Berthomieu (1) , Rafael Mohr (1, 2)

1 PolSys - Polynomial Systems
2 RPTU Kaiserslautern-Landau

We describe a version of the FGLM algorithm that can be used to compute generic fibers of positive-dimensional polynomial ideals. It combines the FGLM algorithm with a Hensel lifting strategy. We show that this algorithm has a complexity quasi-linear in the number of lifting steps. Some provided experimental data also demonstrates the practical efficacy of our algorithm. Additionally, we sketch a related Hensel lifting method to compute Gröbner bases using so-called tracers.

Domaines: Calcul formel [cs.SC]; Algèbre commutative [math.AC]

Jérémy Berthomieu, Rafael Mohr. Computing Generic Fibres of Polynomial Ideals with FGLM and Hensel Lifting. 2024. ⟨hal-04440914⟩