RealComprehensiveTriangularize

Solving parametric polynomial systems by RealComprehensiveTriangularize. In the authors’ previous work [J. Symb. Comput. 47, No. 6, 610--642 (2012; Zbl 1264.12011)], the concept of comprehensive triangular decomposition of parametric semi-algebraic systems (RCTD for short) was introduced. For a given parametric semi-algebraic system, say S, an RCTD partitions the parametric space into disjoint semi-algebraic sets, above each of which the real solutions of S are described by a finite family of triangular systems. Such a decomposition permits to easily count the number of distinct real solutions depending on different parameter values as well as to conveniently describe the real solutions as continuous functions of the parameters. In this paper, we present the implementation of RCTD in the RegularChains library, namely the RealComprehensiveTriangularize command. The use of RCTD is illustrated by the stability analysis of several biological systems.