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Journal of Systems Science and Complexity

, Volume 32, Issue 1, pp 37–46

# Characteristic Decomposition: From Regular Sets to Normal Sets

• Chenqi Mou
• Dongming Wang
Article

## 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.

## Keywords

Characteristic decomposition characteristic pair normal set regular set,W-characteristic set

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## Notes

### 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.

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## Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2019

## Authors and Affiliations

1. 1.LMIB – School of Mathematics and Systems Science/Beijing Advanced Innovation Center for Big Data and Brain ComputingBeihang UniversityBeijingChina
2. 2.LMIB – SKLSDE – School of Mathematics and Systems Science/Beijing Advanced Innovation Center for Big Data and Brain ComputingBeihang UniversityBeijingChina
3. 3.Centre National de la Recherche ScientifiqueParis cedex 16France