MITACS Seminar Series on Mathematics of Computer Algebra and Analysis
Solving parametric polynomial systems with the RegularChains library in Maple.
Wei Pan, University of Western Ontario
Abstract: Solving polynomial systems with parameters has become an increasing need in several applied areas such as robotics, geometric modeling, stability analysis of dynamical systems and others. These questions have been approached by various techniques including comprehensive Groebner bases, and triangular decompositions. The notion of a comprehensive triangular decomposition (CTD), introduced by C. Chen, O. Golubitsky, F. Lemaire, M. Moreno Maza and W. Pan (CASC 2007) combines the advantages of these previous techniques. An algorithm for computing CTDs has also been proposed by the authors. Its implementation within the RegularChains library has led to two new modules that we shall demonstrate in this talk. The first one offers functionalities to manipulate constructible sets. The second one provides tools for studying parametric polynomial systems.