English

Computing Generic Fibers of Polynomial Ideals with FGLM and Hensel Lifting

Symbolic Computation 2024-09-20 v2 Commutative Algebra

Abstract

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. In analogy with Hensel lifting, we show that this algorithm has a complexity quasi-linear in the number of terms of certain m\mathfrak{m}-adic expansions we compute. Some provided experimental data also demonstrates the practical efficacy of our algorithm.

Keywords

Cite

@article{arxiv.2402.03144,
  title  = {Computing Generic Fibers of Polynomial Ideals with FGLM and Hensel Lifting},
  author = {Jérémy Berthomieu and Rafael Mohr},
  journal= {arXiv preprint arXiv:2402.03144},
  year   = {2024}
}