Invariants for the computation of intransitive and transitive Galois groups
type: Item
instance of: scholarly article
title: Invariants for the computation of intransitive and transitive Galois groups
zbMATH Open document ID: 1257.12006
author: Andreas-Stephan Elsenhans
published in: Journal of Symbolic Computation
publication date: 2012-03-22T00:00:00Z
review text: An important step in algorithms based on Stauduhar's approach for computing the Galois group of a polynomial over \(\mathbb{Z}\) is the computation of relative invariant polynomials. Most results on this step deal with the computation of invariants for transitive groups. The case of intransitive groups is reduced to the transitive case, often resulting in invariants that are too large to handle in practice. In this paper, the author describes a method using subdirect products to compute invariants in the intransitive case directly, as opposed to reducing to the transitive case. Numerical results demonstrate that the new method can be applied successfully in the majority of cases.
reviewed by: Michael J. Jacobson jun.
Mathematics Subject Classification ID: 12Y05
Mathematics Subject Classification ID: 11R32
Mathematics Subject Classification ID: 12F10
zbMATH DE Number: 6017592
zbMATH Keywords: Galois group
zbMATH Keywords: invariant polynomial
zbMATH Keywords: intransitive subgroup
zbMATH Keywords: representation theory
zbMATH Keywords: algorithm
describes a project that uses: Magma
MaRDI profile type: Publication
full work available at URL: j.jsc.2011.11.006
OpenAlex ID: W2037628886
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DOI: 10.1016/J.JSC.2011.11.006
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description: scientific article; zbMATH DE number 6017592