Computing Generic Fibers of Polynomial Ideals with FGLM and Hensel Lifting - Archive ouverte HAL
Communication Dans Un Congrès Année : 2024

Computing Generic Fibers of Polynomial Ideals with FGLM and Hensel Lifting

Jérémy Berthomieu
Rafael Mohr
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Résumé

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.
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Dates et versions

hal-04440914 , version 1 (06-02-2024)
hal-04440914 , version 2 (11-09-2024)

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Jérémy Berthomieu, Rafael Mohr. Computing Generic Fibers of Polynomial Ideals with FGLM and Hensel Lifting. 49th International Symposium on Symbolic and Algebraic Computation, Jul 2024, Raleigh, NC, United States. pp.307-315, ⟨10.1145/3666000.3669703⟩. ⟨hal-04440914v2⟩
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