Fraction-free algorithm for the computation of diagonal forms matrices over Ore domains using Gröbner bases

DOI10.1016/j.jsc.2011.12.042zbMath1245.65051arXiv1110.5468OpenAlexW2039757247MaRDI QIDQ432750

Viktor Levandovskyy, Kristina Schindelar

Publication date: 4 July 2012

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.5468

zbMATH Keywords

matrix normal formdecoupling of systems of functional equationsfraction-free algorithmmatrix diagonalisation over ringsnon-commutative Gröbner basisOre localization

Mathematics Subject Classification ID

Related Items (1)

Basic Module Theory over Non-commutative Rings with Computational Aspects of Operator Algebras

Uses Software

• Plural
• SINGULAR
• OreModules
• Janet
• EDIM

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Serre's reduction of linear partial differential systems with holonomic adjoints
• Computing diagonal form and Jacobson normal form of a matrix using Gröbner bases
• A fast Las Vegas algorithm for computing the Smith normal form of a polynomial matrix
• Complexity of factoring and calculating the GCD of linear ordinary differential operators
• Elimination orderings and localization in PBW algebras.
• Gröbner bases and primary decomposition of polynomial ideals
• Non-commutative elimination in Ore algebras proves multivariate identities
• On the computation of elementary divisors of integer matrices
• Fraction-free row reduction of matrices of Ore polynomials.
• Factoring and decomposing a class of linear functional systems
• OreModules: A Symbolic Package for the Study of Multidimensional Linear Systems
• Time-varying polynomial matrix systems
• An algebraic analysis approach to linear time-varying systems
• A Behavioral Approach to Time-Varying Linear Systems. Part 1: General Theory
• Mr. Smith goes to Las Vegas: Randomized parallel computation of the Smith Normal form of polynomial matrices

This page was built for publication: Fraction-free algorithm for the computation of diagonal forms matrices over Ore domains using Gröbner bases