Generic regular decompositions for generic zero-dimensional systems

Two new concepts,generic regular decomposition and regular-decomposition-unstable（RDU） variety for generic zero-dimensional systems,are introduced in this paper and an algorithm is proposed for computing a generic regular decomposition and the associated RDU variety of a given generic zero-dimensional system simultaneously. The solutions of the given system can be expressed by finitely many zero-dimensional regular chains if the parameter value is not on the RDU variety. The so called weakly relatively simplicial decomposition plays a crucial role in the algorithm,which is based on the theories of subresultants. Furthermore,the algorithm can be naturally adopted to compute a non-redundant Wu＇s decomposition and the decomposition is stable at any parameter value that is not on the RDU variety. The algorithm has been implemented with Maple 16 and experimented with a number of benchmarks from the literature. Empirical results are also presented to show the good performance of the algorithm.