El Polinomio de Bernstein-Sato de una singularidad

Abstract

The Bernstein-Sato polynomial or the 푏-function is an important invariant in singular theory. It is closely related to di erentials operators. This polynomial has very useful properties and applications in di erents elds of mathematics. It was introduced in the early 1970s simultaneously by Joseph Bernstein and Mikio Sato. In this Final Degree Project we study the proof of the existence of the BernsteinSato polynomial over the Weyl Algebra, in addition, we study some of the libraries and commands in the computational algebra systems Macaulay2 and Singular related to D-modules and some of the algorithms on which these commands are based on. Finally we conclude the work adding a series of examples of computations of the Bernstein-Sato polynomial and making a small comparison of e ectiveness between both programs.