On the verification of polynomial system solvers

Abstract. We discuss the verification of mathematical software solving polynomial systems symbolically by way of triangular decomposition. Standard verification techniques are highly resource consuming and apply only to polynomial systems which are easy to solve. We exhibit a new approach which manipulates constructible sets represented by regular systems. We provide comparative benchmarks of different verification procedures applied to four solvers on a large set of well-known polynomial systems. Our experimental results illustrate the high efficiency of our new approach. In particular, we are able to verify triangular decompositions of polynomial systems which are not easy to solve. Key words: Software verification, polynomial system solver, triangular decomposition.

• Type: Journal
• Year: 2008
• Where: FCSC
• Authors: Changbo Chen, Marc Moreno Maza, Wei Pan, Yuzhen Xie
• Keywords: FCSC 2008, Polynomial Systems, Standard Verification Techniques, Triangular Decomposition