Some properties of triangular sets and improvement upon algorithm charser

Authors:
Yong-Bin Li
Affiliations:
Chengdu Institute of Computer Applications, Chinese Academy of Sciences, Chengdu, Sichuan, China
Venue:
AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
Year:
2006

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Abstract

We present some new properties of triangular sets, which have rather theoretical contribution to understand the structure of the affine varieties of triangular sets. Based on these results and the famous algorithm CharSet, we present two modified versions of the algorithm CharSer that can decompose any nonempty polynomial set into characteristic series. Some examples show that our improvement can efficiently avoid for redundant decompositions, and reduce the branches of the decomposition tree at times.