Algorithms for Computing Triangular Decompositions of Polynomial Systems
Symbolic Computation
2011-04-06 v1 Mathematical Software
Abstract
We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which permits to greatly simplify and optimize the sub-algorithms. Extracting common work from similar expensive computations is also a key feature of our algorithms. In our experimental results the implementation of our new algorithms, realized with the {\RegularChains} library in {\Maple}, outperforms solvers with similar specifications by several orders of magnitude on sufficiently difficult problems.
Cite
@article{arxiv.1104.0689,
title = {Algorithms for Computing Triangular Decompositions of Polynomial Systems},
author = {Changbo Chen and Marc Moreno Maza},
journal= {arXiv preprint arXiv:1104.0689},
year = {2011}
}