Abstract
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.
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Tang, X., Chen, Z. & Xia, B. Generic regular decompositions for generic zero-dimensional systems. Sci. China Inf. Sci. 57, 1–14 (2014). https://doi.org/10.1007/s11432-013-5057-5
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DOI: https://doi.org/10.1007/s11432-013-5057-5