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Generic regular decompositions for parametric polynomial systems

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Abstract

This paper presents a generalization of the authors’ earlier work. In this paper, the two concepts, generic regular decomposition (GRD) and regular-decomposition-unstable (RDU) variety introduced in the authors’ previous work for generic zero-dimensional systems, are extended to the case where the parametric systems are not necessarily zero-dimensional. An algorithm is provided to compute GRDs and the associated RDU varieties of parametric systems simultaneously on the basis of the algorithm for generic zero-dimensional systems proposed in the authors’ previous work. Then the solutions of any parametric system can be represented by the solutions of finitely many regular systems and the decomposition is stable at any parameter value in the complement of the associated RDU variety of the parameter space. The related definitions and the results presented in the authors’ previous work are also generalized and a further discussion on RDU varieties is given from an experimental point of view. The new algorithm has been implemented on the basis of DISCOVERER with Maple 16 and experimented with a number of benchmarks from the literature.

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Authors and Affiliations

  1. School of Mathematical Sciences, Peking University, Beijing, 100084, China

    Zhenghong Chen, Xiaoxian Tang & Bican Xia

Authors
  1. Zhenghong Chen
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  2. Xiaoxian Tang
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  3. Bican Xia
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Corresponding author

Correspondence to Zhenghong Chen.

Additional information

This research is supported by by the National Natural Science Foundation of China under Grant Nos. 11271034, 11290141, and the Project SYSKF1207 from SKLCS, IOS, the Chinese Academy of Sciences.

This paper was recommended for publication by Editor LI Ziming.

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Chen, Z., Tang, X. & Xia, B. Generic regular decompositions for parametric polynomial systems. J Syst Sci Complex 28, 1194–1211 (2015). https://doi.org/10.1007/s11424-015-3015-6

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  • DOI: https://doi.org/10.1007/s11424-015-3015-6

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