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.Ministerio de Ciencia y TecnologíaJunta de Andalucí
