Multi-modular algorithm for computing the splitting field of a polynomial

Guénaël Renault, Kazuhiro Yokoyama

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

Abstract

Let f be a univariate monic integral polynomial of degree n and let (α1...,αn) be an n-tuple of its roots in an algebraic closure ℚ̄ of ℚ. Obtaining an algebraic representation of the splitting field ℚ (α1...,αn) of f is a question of first importance in effective Galois theory. For instance, it allows us to manipulate symbolically the roots of f. In this paper, we propose a new method based on multi-modular strategy. Actually, we provide algorithms for this task which return a triangular set encoding the splitting ideal of f. We examine the ability/practicality of the method by experiments on a real computer and study its complexity.

Original languageEnglish
Title of host publicationISSAC'08
Subtitle of host publicationProceedings of the 21st International Symposium on Symbolic and Algebraic Computation 2008
Pages247-254
Number of pages8
DOIs
Publication statusPublished - 18 Dec 2008
Externally publishedYes
Event21st Annual Meeting of the International Symposium on Symbolic Computation, ISSAC 2008 - Linz, Hagenberg, Austria
Duration: 20 Jul 200823 Jul 2008

Publication series

NameProceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

Conference

Conference21st Annual Meeting of the International Symposium on Symbolic Computation, ISSAC 2008
Country/TerritoryAustria
CityLinz, Hagenberg
Period20/07/0823/07/08

Keywords

  • Galois theory
  • Splitting field

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