000132072 001__ 132072
000132072 005__ 20240301161205.0
000132072 0247_ $$2doi$$a10.1016/j.jalgebra.2011.12.002
000132072 0248_ $$2sideral$$a75910
000132072 037__ $$aART-2012-75910
000132072 041__ $$aeng
000132072 100__ $$aLevandovskyy, V.
000132072 245__ $$aAlgorithms for checking rational roots of b-functions and their applications
000132072 260__ $$c2012
000132072 5060_ $$aAccess copy available to the general public$$fUnrestricted
000132072 5203_ $$aThe 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 b-function 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 D-module. 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 b-function 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.
000132072 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E15
000132072 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
000132072 590__ $$a0.583$$b2012
000132072 591__ $$aMATHEMATICS$$b143 / 295 = 0.485$$c2012$$dQ2$$eT2
000132072 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000132072 700__ $$0(orcid)0000-0002-6559-4722$$aMartín-Morales, J.
000132072 773__ $$g352, 1 (2012), 408-429$$pJ. algebra$$tJournal of Algebra$$x0021-8693
000132072 8564_ $$s442560$$uhttps://zaguan.unizar.es/record/132072/files/texto_completo.pdf$$yPostprint
000132072 8564_ $$s2316486$$uhttps://zaguan.unizar.es/record/132072/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint
000132072 909CO $$ooai:zaguan.unizar.es:132072$$particulos$$pdriver
000132072 951__ $$a2024-03-01-14:37:08
000132072 980__ $$aARTICLE