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

作     者：LU Dong SUN Yao WANG Dingkang 

作者机构：KLMMAcademy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical SciencesUniversity of Chinese Academy of Sciences SKLOISInstitute of Information EngineeringChinese Academy of Sciences 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2019年第32卷第1期

页      面：234-255页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported in part by the CAS Project QYZDJ-SSW-SYS022 the National Natural Science Foundation of China under Grant No.61877058 the Strategy Cooperation Project AQ-1701 

主　　题：Comprehensive Gröbner basis comprehensive Gröbner system discovering geometric theorems mechanically parametric polynomial system quantifier elimination 

摘      要：Weispfenning in 1992 introduced the concepts of comprehensive Gr?bner system/basis of a parametric polynomial system, and he also presented an algorithm to compute them. Since then,this research ?eld has attracted much attention over the past several decades, and many effcient algorithms have been proposed. Moreover, these algorithms have been applied to many different ?elds,such as parametric polynomial equations solving, geometric theorem proving and discovering, quanti?er 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.