2011/04/04 by Changbo Chen, Chen, Changbo, Marc Moreno Maza +1
Computer Science · Mathematics · #Commutative Algebra and Its Applications #FOS: Computer and information sciences #Formal Methods in Verification #Mathematical Software (cs.MS) #Polynomial and algebraic computation #Symbolic Computation (cs.SC) #cs.MS #cs.SC
paper · pdf · doi:10.48550/arxiv.1104.0689
arxiv created 2011/04/04 · openalex publication_date 2011/04/04 · arxiv updated 2011/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.