Principal intersection and bernstein-sato polynomial of an affine variety

Authors:
Daniel Andres;Viktor Levandovskyy;Jorge Martín Morales
Affiliations:
RWTH Aachen University, Aachen, Germany;RWTH Aachen University, Aachen, Germany;University of Zaragoza, Zaragoza, Spain
Venue:
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Year:
2009

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Abstract

We present a general algorithm for computing an intersection of a left ideal of an associative algebra over a field with a subalgebra, generated by a single element. We show applications of this algorithm in different algebraic situations and describe our implementation in Singular. Among other, we use this algorithm in computational D-module theory for computing e.g. the Bernstein-Sato polynomial of a single polynomial with several approaches. We also present a new method, having no analogues yet, for the computation of the Bernstein-Sato polynomial of an affine variety. Also, we provide a new proof of the algorithm by Briançon-Maisonobe for the computation of the s-parametric annihilator of a polynomial.