Abstract
An algorithm for computing comprehensive Grobner systems (CGS) is introduced in rings of linear partial differential operators. Their applications to b-functions are considered. The resulting algorithm designed for a wide use of computing comprehensive Grobner systems can be used to compute all the roots of b-functions and relevant holonomic D-modules. Furthermore, with our implementation, effective methods are illustrated for computing holonomic D-modules associated with hypersurface singularities. It is shown that the proposed algorithm is full of versatility.
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