Computational methods in algebra and analysis
This paper describes some applications of Computer Algebra to Algebraic Analysis also known as D-module theory, i.e. the algebraic study of the systems of linear partial differential equations. Gröbner bases for rings of linear differential operators are the main tools in the field. We start by givi...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2007 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/41156 |
| Acceso en línea: | http://hdl.handle.net/11441/41156 |
| Access Level: | acceso abierto |
| Palabra clave: | Polynomial ring polynomial system ring of linear differential operators differential system D-module Gröbner basis division theorem characteristic variety irregularity Bernstein-Sato polynomial logarithmic Dmodule projective module syzygy free resolution |
| Sumario: | This paper describes some applications of Computer Algebra to Algebraic Analysis also known as D-module theory, i.e. the algebraic study of the systems of linear partial differential equations. Gröbner bases for rings of linear differential operators are the main tools in the field. We start by giving a short review of the problem of solving systems of polynomial equations by symbolic methods. These problems motivate some of the later developed subjects. |
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