A Survey on Algorithms for Computing Comprehensive Grobner Systems and Comprehensive Grobner Bases

Weispfenning in 1992 introduced the concepts of comprehensive Grobner system/basis of a parametric polynomial system, and he also presented an algorithm to compute them. Since then, this research field has attracted much attention over the past several decades, and many efficient algorithms have been proposed. Moreover, these algorithms have been applied to many different fields, such as parametric polynomial equations solving, geometric theorem proving and discovering, quantifier elimination, and so on. This survey brings together the works published between 1992 and 2018, and we hope that this survey is valuable for this research area.