Computing Generic Fibers of Polynomial Ideals with FGLM and Hensel Lifting
<|reference_start|>Computing Generic Fibers of Polynomial Ideals with FGLM and Hensel Lifting: 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 $\mathfrak{m}$-adic expansions we compute. Some provided experimental data also demonstrates the practical efficacy of our algorithm.<|reference_end|>
@article{berthomieu2024computing,
    title={Computing Generic Fibers of Polynomial Ideals with FGLM and Hensel
  Lifting},
    author={J'er'emy Berthomieu, Rafael Mohr},
    journal={49th International Symposium on Symbolic and Algebraic
  Computation, Jul 2024, Raleigh, NC, United States. pp.307-315},
    year={2024},
    doi={10.1145/3666000.3669703},
    archivePrefix={arXiv},
    eprint={2402.03144},
    primaryClass={cs.SC math.AC}
}