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 Gr\"obner bases using so-called tracers.

翻译：本文描述了一种可计算正维多项式理想通用纤维的FGLM算法变体。该算法将FGLM算法与Hensel提升策略相结合。我们证明该算法的复杂度与提升步数呈拟线性关系。提供的实验数据也展示了该算法的实际有效性。此外，我们概述了一种通过所谓追踪器计算Gröbner基的相关Hensel提升方法。