Computing Logarithmic Vector Fields Associated with Parametric Semi-Quasihomogeneous Hypersurface Isolated Singularities

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Logarithmic vector fields associated with parametric semi-quasihomogeneous hypersurface isolated singularities are considered in the context of symbolic computation. A new algorithm for computing the logarithmic vector fields is introduced. The keys of this approach are the concept of a polar variety and parametric local cohomology systems. The resulting algorithm also provides a decomposition of the parameter space depending on the structure of the logarithmic vector fields.