A modular method for computing the splitting field of a polynomial

Guénaël Renault, Kazuhiro Yokoyama

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We provide a modular method for computing the splitting field K f of an integral polynomial f by suitable use of the byproduct of computation of its Galois group Gf by p-adic Stauduhar's method. This method uses the knowledge of Gf with its action on the roots of f over a p-adic number field, and it reduces the computation of Kf to solving systems of linear equations modulo some powers of p and Hensel liftings. We provide a careful treatment on reducing computational difficulty. We examine the ability/practicality of the method by experiments on a real computer and study its complexity.

Original languageEnglish
Title of host publicationAlgorithmic Number Theory - 7th International Symposium, ANTS-VII, Proceedings
PublisherSpringer Verlag
Pages124-140
Number of pages17
ISBN (Print)3540360751, 9783540360759
DOIs
Publication statusPublished - 1 Jan 2006
Externally publishedYes
Event7th International Symposium on Algorithmic Number Theory, ANTS-VII - Berlin, Germany
Duration: 23 Jul 200628 Jul 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4076 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference7th International Symposium on Algorithmic Number Theory, ANTS-VII
Country/TerritoryGermany
CityBerlin
Period23/07/0628/07/06

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