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

doi:10.1007/s11424-019-8357-z

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	A Survey on Algorithms for Computing Comprehensive Grobner Systems and Comprehensive Grobner Bases
	Lu Dong 1,2; Sun Yao 3; Wang Dingkang1,2
	2019-02-01
发表期刊	JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
ISSN	1009-6124
卷号	32 期号:1 页码:234-255
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.
关键词	Comprehensive Grobner basis comprehensive Grobner system discovering geometric theorems mechanically parametric polynomial system quantifier elimination
DOI	10.1007/s11424-019-8357-z
语种	英语
资助项目	CAS Project[QYZDJ-SSW-SYS022] ; National Natural Science Foundation of China[61877058] ; Strategy Cooperation Project[AQ-1701]
WOS研究方向	Mathematics
WOS类目	Mathematics, Interdisciplinary Applications
WOS记录号	WOS:000458795500013
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/32585
专题	系统科学研究所
通讯作者	Lu Dong
作者单位	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
推荐引用方式 GB/T 7714	Lu Dong,Sun Yao,Wang Dingkang. A Survey on Algorithms for Computing Comprehensive Grobner Systems and Comprehensive Grobner Bases[J]. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,2019,32(1):234-255.
APA	Lu Dong,Sun Yao,&Wang Dingkang.(2019).A Survey on Algorithms for Computing Comprehensive Grobner Systems and Comprehensive Grobner Bases.JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,32(1),234-255.
MLA	Lu Dong,et al."A Survey on Algorithms for Computing Comprehensive Grobner Systems and Comprehensive Grobner Bases".JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY 32.1(2019):234-255.