### COMPUTATIONAL METHODS IN ALGEBRA AND ANALYSIS

*F. J. Castro-Jiménez*

#### Resumen

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.

**Key words:**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.**AMS subject classifications:**68W30 13D02 13Pxx 14Qxx 16S32 16Z05 32C38 33F10.Texto completo: PDF