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
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
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.