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Characteristic Decomposition: From Regular Sets to Normal Sets

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Abstract

In this paper it is shown how to transform a regular triangular set into a normal triangular set by computing the W-characteristic set of their saturated ideal and an algorithm is proposed for decomposing any polynomial set into finitely many strong characteristic pairs, each of which is formed with the reduced lexicographic Gr¨obner basis and the normal W-characteristic set of a characterizable ideal.

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Acknowledgements

The authors wish to thank an anonymous referee who pointed out some unclarity in an early version of the proof of Theorem 4.4 and provided the authors with helpful suggestions for improving the paper.

Author information

Authors and Affiliations

  1. LMIB – School of Mathematics and Systems Science/Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, 100191, China

    Chenqi Mou

  2. LMIB – SKLSDE – School of Mathematics and Systems Science/Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, 100191, China

    Dongming Wang

  3. Centre National de la Recherche Scientifique, 75794, Paris cedex 16, France

    Dongming Wang

Authors
  1. Chenqi Mou
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  2. Dongming Wang
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Corresponding author

Correspondence to Chenqi Mou.

Additional information

The authors dedicate this article to the memory of Wen-Tsün Wu (1919—2017), with deep gratitude for his influence and advice. The described work was supported partially by the National Natural Science Foundation of China under Grant Nos. 11771034 and 11401018.

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Mou, C., Wang, D. Characteristic Decomposition: From Regular Sets to Normal Sets. J Syst Sci Complex 32, 37–46 (2019). https://doi.org/10.1007/s11424-019-8356-0

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  • DOI: https://doi.org/10.1007/s11424-019-8356-0

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