Details:
Title  Hierarchical comprehensive triangular decomposition.  Author(s)  Zhenghong Chen, Xiaoxian Tang, Bican Xia  Type  Book, Chapter in Book, Conference Proceeding  Abstract  The concept of comprehensive triangular decomposition (CTD) was first introduced by Chen et al. in their CASC’2007 paper and could be viewed as an analogue of comprehensive Gröbner systems for parametric polynomial systems. The first complete algorithm for computing CTD was also proposed in that paper and implemented in the RegularChains library in Maple. Following our previous work on generic regular decomposition for parametric polynomial systems, we introduce in this paper a socalled hierarchical strategy for computing CTDs. Roughly speaking, for a given parametric system, the parametric space is divided into several subspaces of different dimensions and we compute CTDs over those subspaces one by one. So, it is possible that, for some benchmarks, it is difficult to compute CTDs in reasonable time while this strategy can obtain some “partial” solutions over some parametric subspaces. The program based on this strategy has been tested on a number of benchmarks from the literature. Experimental results on these benchmarks with comparison to RegularChains are reported and may be valuable for developing more efficient triangularization tools.  Keywords  Comprehensive triangular decomposition, regular chain, hierarchical, generic regular decomposition, parametric polynomial system  ISBN  9783662441985/pbk 
URL 
http://link.springer.com/chapter/10.1007%2F9783662441992_66 
Language  English  Pages  434441  Publisher  Berlin: Springer  Year  2014  Edition  0  Translation 
No  Refereed 
No 
