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arXiv · 1208.6112

Generic Regular Decompositions for Generic Zero-Dimensional Systems

Xiaoxian Tang·Zhenghong Chen·Bican Xia
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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 subresultant chains. 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 15 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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Xiaoxian Tang, Zhenghong Chen, Bican Xia. 2013-01-16. Generic Regular Decompositions for Generic Zero-Dimensional Systems. https://arxiv.org/abs/1208.6112

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