Aspectos computacionales del Polinomio de Bernstein-Sato de una singularidad

Abstract

The Bernstein-Sato polynomial or the b-function is an important invariant in singularity theory. It is closely related to diferentials operators. This polynomial has very useful properties and applications in diferents fields of mathematics. It was introduced in the early 1970s simultaneously, but under diferent scopes, by Joseph Bernstein and Mikio Sato. The purpose of this Master Thesis Dissertation is an update and an overview of the main tools and results on which the algorithmic study of b-function is based. In addition, we study some of the most efficient algorithms for computing b-functions to date, implemented in algebraic systems such as Singular/Plural or Risa/Asir.