Computation methods of logarithmic vector fields associated to semi-weighted homogeneous isolated hypersurface singularities

Abstract

Methods for computing logarithmic vector fields along a semi-weighted homogeneous hypersurface with an isolated singularity are considered in the context of symbolic computation. The main idea of our approach is based on the concept of polar variety and of algebraic local cohomology. New algorithms are introduced for computing a set of generators of the modules of logarithmic vector fields. The keys of the resulting algorithms are a notion of parametric syzygy system and that of parametric local cohomology system.