Stability of Triangular Decomposition and Comprehensive Triangular Decomposition
Abstract
A new concept, decompositionunstable (DU) variety of a parametric polynomial system, is introduced in this paper and the stabilities of several triangular decomposition methods, such as characteristic set decomposition, relatively simplicial decomposition and regular chain decomposition, for parametric polynomial systems are discussed in detail. The concept leads to a definition of weakly comprehensive triangular decomposition (WCTD) and a new algorithm for computing comprehensive triangular decomposition (CTD) which was first introduced in [4] for computing an analogue of comprehensive Groebner systems for parametric polynomial systems. Our algorithm takes advantage of a hierarchical solving strategy and a selfadaptive order of parameters. The algorithm has been implemented with Maple 15 and experimented with a number of benchmarks from the literature. Comparison with the Maple package RegularChains, which contains an implementation of the algorithm in [4], is provided and the results illustrate that the time costs by our program for computing CTDs of most examples are no more than those by RegularChains.
 Publication:

arXiv eprints
 Pub Date:
 October 2011
 DOI:
 10.48550/arXiv.1110.6275
 arXiv:
 arXiv:1110.6275
 Bibcode:
 2011arXiv1110.6275T
 Keywords:

 Computer Science  Symbolic Computation;
 Mathematics  Algebraic Geometry
 EPrint:
 This paper has been withdrawn by the author due to a crucial error in a proof