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...

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Bibliographic Details
Published in:	arXiv.org
Main Authors:	Berthomieu, Jérémy, Mohr, Rafael
Format:	Paper
Language:	English
Published:	Ithaca Cornell University Library, arXiv.org 19.09.2024
Subjects:	Algorithms Hoisting Polynomials
ISSN:	2331-8422
Online Access:	Get full text
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Summary:	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.
Bibliography:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.2402.03144