First presenter Co-presenter(s)
Name :  Changbo  Chen * Name:  Marc Moreno Maza *
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Affiliation: University of Western Ontario Name:   et al.
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Country: Canada Name:   
14-05  E-mail:    
Session: 14- Algorithms for Parametric Systems and their Applications Schedule:
Thursday, 14:00
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Title of
Solving Parametric Polynomial Systems with the RegularChains Library in Maple

Changbo Chen and Marc Moreno Maza, in collaboration with Francois Lemaire, Bican Xia, Rong Xiao and Yuzhen Xie.

Solving systems of parametric polynomial equations symbolically is in demand for an increasing number of applications such as program verification, optimization and the study of dynamical systems. Groebner bases and triangular decompositions are classical techniques for processing parametric systems. Recent research has focused on enhancing theories and algorithms to meet the practical requirement of these systems. The ParametricSystemTools module of the RegularChains library in Maple implements comprehensive triangular decompositions (CTD) and real root classification (RRC) which are tools dedicated to study polynomial systems with parameters. It is supported by the modules ConstructibleSetTools and SemiAlgebraicSetTools. The first one provides useful commands for solving over the complex numbers and the second over the reals. This talk is an overview of the functionalities of these three modules. We start with a review of the fundamental concepts of CTD, RRC and Border Polynomial together with their relation with other popular notions for parametric polynomial systems. We consider then applications from program verification and biochemistry. In this latter case, we will combine our library with software tools for modeling.