We will first introduce the definition of the Comprehensive Groebner System (CGS) and present efficient algorithms to compute the CGS of a parametric polynomial system. We will also outline key applications of CGS, such as solving parametric polynomial equation systems, automatic geometric theorem discovery, and quantifier elimination over an algebraically closed field.
Wang Dingkang is a researcher at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, with prolific achievements in areas such as automated geometric theorem proving and symbolic computation. Together with his collaborators, he resolved the spatial geometry "Pyramid" problem, a geometric problem proposed by the renowned mathematician Zassenhaus, and the problem of smooth blending of algebraic surfaces. He introduced efficient algorithms for computing parametric Groebner systems and developed novel methods for the automated discovery of geometric theorems. He also devised signature-based standard basis algorithms for polynomial systems under arbitrary term orders and solved a series of mathematical problems related to parametric polynomial systems, including algorithms for extending GCDs of parametric univariate polynomials, GCDs of parametric multivariate polynomials, rational representations of zero-dimensional ideals in parametric cases, and the parametric version of the Quillen-Suslin theorem. Furthermore, he has been invited to deliver plenary talks at numerous international conferences and has published over 30 high-quality academic papers in top-tier international conferences and journals in symbolic computation.
