Algorithm for computing local Bernstein-Sato ideals

TL;DR

This paper introduces an algorithm to compute local Bernstein-Sato ideals at a point and to stratify the space so that these ideals are constant on each stratum, demonstrated with non-trivial examples.

Contribution

The paper presents a novel algorithm for computing local Bernstein-Sato ideals and their stratification, advancing computational methods in algebraic analysis.

Findings

Successfully computes local Bernstein-Sato ideals at given points.

Provides a constructible stratification where ideals are constant.

Demonstrates the algorithm with complex, non-trivial examples.

Abstract

Given $p$ polynomials of $n$ variables over a field $k$ of characteristic 0 and a point $a \in k^n$, we propose an algorithm computing the local Bernstein-Sato ideal at $a$. Moreover with the same algorithm we compute a constructible stratification of $k^n$ such that the local Bernstein-Sato ideal is constant along each stratum. Finally, we present non-trivial examples computed with our algorithm.