Comprehensive Gröbner systems in PBW algebras, Bernstein–Sato ideals and holonomic D-modules. (November 2018)

• Record Type: Journal Article
• Authors: Nabeshima, Katsusuke; Ohara, Katsuyoshi; Tajima, Shinichi
• Is Part Of: Journal of symbolic computation. Volume 89(2018)
• Page Start: 146
• Page End: 170
• Publication Date: 2018-11
• Subjects: 13D45 -- 32C37 -- 13J05 -- 32A27; Comprehensive Gröbner systems -- Poincaré–Birkhoff–Witt algebras -- Bernstein–Sato ideals -- Holonomic D-modules; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2017.11.010
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: A computation method of comprehensive Gröbner systems is introduced in Poincaré–Birkhoff–Witt (PBW) algebras and applications to Bernstein–Sato ideals, holonomic D -modules for parametric cases are considered. The proposed method provides in particular holonomic D -modules associated with primary components of Bernstein–Sato ideals. Furthermore, with our implementation, effective methods are illustrated for computing b -functions of μ -constant deformations of hypersurface isolated singularities by utilizing holonomic D -modules. High versatility of the proposed method is also illustrated by several examples.