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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Detalles Bibliográficos
Autor: Castro Jiménez, Francisco Jesús
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
Descripción
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.