Comprehensive Gröbner systems in PBW algebras, Bernstein-Sato ideals and holonomic D-modules

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.