An algorithm of computing $b$-functions

TL;DR: In this paper, a relation between Bernstein-Sato ideals and local systems is proposed and partially confirmed, which gives yet a different point of view on the nature of the structure of cohomology support loci of local systems.

TL;DR: A numerical invariant for rings of characteristic zero or p>0 that exhibits many of the useful properties of the F-signature and a number of results on symbolic powers and Bernstein-Sato polynomials are obtained.

TL;DR: The main purpose of this paper is to present algorithms for computing a holonomic system for the definite integral of aholonomic function with parameters over a domain defined by polynomial inequalities.

TL;DR: A modification of Budur–Mustaţaˇ–Saito’s generalized Bernstein–Sato polynomial is defined, which is a modification of budur-musta-Musta-Saito's generalized Bernstein-SatoPolynomial in Grobner bases in Weyl algebras.

TL;DR: In this article, the authors present algorithms that compute certain local cohomology modules associated to ideals in a ring of polynomials containing the rational numbers, which is based on the theory of D-modules.

TL;DR: In this paper, the zéros de b sont rationnels, i.e., the valeurs propres de la monodromie sont les g-2î7i-ûs.