Towards an efficient meat-axe algorithm using \(f\)-cyclic matrices: The density of uncyclic matrices in M\((n,q)\)
type: Item
instance of: scholarly article
title: Towards an efficient meat-axe algorithm using \(f\)-cyclic matrices: The density of uncyclic matrices in M\((n,q)\)
zbMATH Open document ID: 1179.65005
author: Cheryl E. Praeger
author: S. P. Glasby
published in: Journal of Algebra
publication date: 2009-10-02T00:00:00Z
review text: This is a continuation of research of the meat-axe algorithm using \(f\)-cyclic matrices, see \textit{S. P. Glasby} [J. Algebra 300, No.~1, 77--90 (2006; Zbl 1108.15015)]. The lower and upper bounds for the density of uncyclic matrices in \(\text{M}(n,\mathbb{F}_q)\) are obtained. The authors give a practical Monte Carlo algorithm to test whether a given matrix is \(f\)-cyclic relative to some irreducible divisor of its characteristic polynomial. Also the algorithm outputs a witness vector which can be used when applying Norton's irreducibility test; see \textit{D. F. Holt} and \textit{S. Rees} [J. Aust. Math. Soc., Ser. A 57, No.~1, 1--16 (1994; Zbl 0833.20021)]. The work is written understandable for nonspecialists; the references to available programs are present.
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 15B05
zbMATH DE Number: 5610504
zbMATH Keywords: complexity analysis
zbMATH Keywords: meat-axe algorithm
zbMATH Keywords: \(f\)-cyclic matrices
zbMATH Keywords: uncyclic matrices
zbMATH Keywords: Monte Carlo algorithm
zbMATH Keywords: Norton's irreducibility test
describes a project that uses: GAP
describes a project that uses: MeatAxe
describes a project that uses: Magma
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2009.02.021
OpenAlex ID: W2083277604
Wikidata QID: Q56987737
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DOI: 10.1016/J.JALGEBRA.2009.02.021
description: scientific article; zbMATH DE number 5610504