Characteristic Decomposition: From Regular Sets to Normal Sets
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.
KeywordsCharacteristic decomposition characteristic pair normal set regular set,W-characteristic set
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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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