分层综合三角分解
Hierarchical Comprehensive Triangular Decomposition
摘要：
综合三角分解（CTD）的概念首先由Chen等人在他们的CASC'2007论文中引入，并且可以被视为参数多项式系统的综合Grobner系统的模拟。第一个完整的算法计算CTD也提出了在该文件中，并在Maple的RegularChains库中实现。继我们以前的工作一般定期分解参数多项式系统，我们在本文中介绍了一个所谓的分层策略计算CTD。粗略地说，对于一个给定的参数系统，参数空间被划分成几个不同维度的子空间，我们计算CTD在这些子空间一个接一个。因此，这是可能的，对于一些基准，这是很难在合理的时间内计算CTD，而这种策略可以获得一些“部分”的解决方案，在一些参数子空间。该计划的基础上，这一战略已经过测试，从文献中的一些基准。这些基准与RegularChains比较的实验结果报告，可能是有价值的开发更有效的三角化工具。
英文摘要：
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 Grobner 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 so-called hierarchical strategy for computing CTDs. Roughly speaking, for a given parametric system, the parametric space is divided into several sub-spaces of different dimensions and we compute CTDs over those sub-spaces 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 sub-spaces. 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
