Effective algebraic analysis approach to linear systems over Ore algebras
| Autor: | Maris Tõnso, Christoph Koutschan, Alban Quadrat, Thomas Cluzeau |
|---|---|
| Přispěvatelé: | Mathématiques & Sécurité de l'information (XLIM-MATHIS), XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences (OeAW), OUtils de Résolution Algébriques pour la Géométrie et ses ApplicatioNs (OURAGAN), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institute of Cybernetics [Tallinn], Tallinn Technical University |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
0209 industrial biotechnology
Polynomial ring 010102 general mathematics Linear system 02 engineering and technology Symbolic computation 01 natural sciences Noncommutative geometry Algebra Gröbner basis 020901 industrial engineering & automation ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Algebra representation Homological algebra 0101 mathematics [MATH]Mathematics [math] Algebraic analysis Mathematics |
| Zdroj: | Algebraic and Symbolic Computation Methods in Dynamical Systems Algebraic and Symbolic Computation Methods in Dynamical Systems, 9, Springer, pp.4-52, 2020, Advances in Delays and Dynamics, 978-3-030-38355-8 Algebraic and Symbolic Computation Methods in Dynamical Systems ISBN: 9783030383558 |
| Popis: | International audience; The purpose of this chapter is to present a survey on the effective algebraic analysis approach to linear systems theory with applications to control theory and mathematical physics. In particular, we show how the combination of effective methods of computer algebra -- based on Gröbner basis techniques over a class of noncommutative polynomial rings of functional operators called Ore algebras -- and constructive aspects of module theory and homological algebra enables the characterization of structural properties of linear functional systems. Algorithms are given and a dedicated implementation, called OreAlgebraicAnalysis, based on the Mathematica package HolonomicFunctions, is demonstrated. |
| Databáze: | OpenAIRE |
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