Details:
Title  Algorithms for checking rational roots of bfunctions and their applications  Author(s)  Viktor Levandovskyy, J. MartínMorales  Type  Article in Journal  Abstract  The Bernstein–Sato polynomial of a hypersurface is an important object with many applications. However, its computation is hard, as a number of open questions and challenges indicate. In this paper we propose a family of algorithms called checkRoot for optimized checking whether a given rational number is a root of Bernstein–Sato polynomial and in the affirmative case, computing its multiplicity. These algorithms are used in the new approach to compute the global or local Bernstein–Sato polynomial and bfunction of a holonomic ideal with respect to a weight vector. They can be applied in numerous situations, where a multiple of the Bernstein–Sato polynomial can be established. Namely, a multiple can be obtained by means of embedded resolution, for topologically equivalent singularities or using the formula of AʼCampo and spectral numbers. We also present approaches to the logarithmic comparison problem and the intersection homology Dmodule. Several applications are presented as well as solutions to some challenges which were intractable with the classical methods. One of the main applications is the computation of a stratification of affine space with the local bfunction being constant on each stratum. Notably, the algorithm we propose does not employ primary decomposition. Our results can be also applied for the computation of Bernstein–Sato polynomials for varieties. The examples in the paper have been computed with our implementation of the methods described in Singular:Plural.  Keywords  Singularity, Dmodule, Bernstein–Sato polynomial, Noncommutative Gröbner basis  ISSN  00218693 
URL 
http://www.sciencedirect.com/science/article/pii/S0021869311006855 
Language  English  Journal  Journal of Algebra  Volume  352  Number  1  Pages  408  429  Year  2012  Edition  0  Translation 
No  Refereed 
No 
