Fraction-free algorithm for the computation of diagonal forms matrices over Ore domains using Gröbner bases
type: Item
instance of: scholarly article
title: Fraction-free algorithm for the computation of diagonal forms matrices over Ore domains using Gröbner bases
zbMATH Open document ID: 1245.65051
author: V. Levandovskyy
author: Kristina Schindelar
published in: Journal of Symbolic Computation
publication date: 2012-07-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/1110.5468
review text: The authors present a new fraction-free algorithm for the computation of a diagonal form of a matrix over a certain non-commutative Euclidean domain over a computable field with the help of Gröbner bases. They investigate Ore localizations of common operator algebras over \(K[x]\) and use them in the unimodularity analysis of transformation matrices \(U\) and \(V\). Their algorithm, which is implemented in the computer algebra system \texttt{SINGULAR:PLURAL} following the fraction-free strategy, shows impressive performance compared with methods which directly use fractions.
reviewed by: Constantin Popa
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 13P10
zbMATH DE Number: 6053102
zbMATH Keywords: matrix normal form
zbMATH Keywords: matrix diagonalisation over rings
zbMATH Keywords: Ore localization
zbMATH Keywords: non-commutative Gröbner basis
zbMATH Keywords: decoupling of systems of functional equations
zbMATH Keywords: fraction-free algorithm
describes a project that uses: SINGULAR
describes a project that uses: EDIM
describes a project that uses: Plural
describes a project that uses: OreModules
describes a project that uses: Janet
MaRDI profile type: Publication
OpenAlex ID: W2039757247
arXiv ID: 1110.5468
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DOI: 10.1016/J.JSC.2011.12.042
description: scientific article; zbMATH DE number 6053102