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

被引：4
|
作者：
Lu Dong [1 ,2 ]
Sun Yao [3 ]
Wang Dingkang [1 ,2 ]
机构：
[1] Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China
[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
[3] Chinese Acad Sci, Inst Informat Engn, SKLOIS, Beijing 100093, Peoples R China
来源：
JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY | 2019年 / 32卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Comprehensive Grobner basis; comprehensive Grobner system; discovering geometric theorems mechanically; parametric polynomial system; quantifier elimination;
D O I：
10.1007/s11424-019-8357-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页码：234 / 255
页数：22
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