Automated Reducible Geometric Theorem Proving and Discovery by Grobner Basis Method

doi:10.1007/s10817-016-9395-z

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	Automated Reducible Geometric Theorem Proving and Discovery by Grobner Basis Method
	Zhou, Jie 1; Wang, Dingkang2 ; Sun, Yao 3
	2017-10-01
发表期刊	JOURNAL OF AUTOMATED REASONING
ISSN	0168-7433
卷号	59 期号:3 页码:331-344
摘要	In this paper, we investigate the problem that the conclusion is true on some components of the hypotheses for a geometric statement. In that case, the affine variety associated with the hypotheses is reducible. A polynomial vanishes on some but not all the components of a variety if and only if it is a zero divisor in a quotient ring with respect to the radical ideal defined by the variety. Based on this fact, we present an algorithm to decide if a geometric statement is generally true or generally true on components by the Grobner basis method. This method can also be used in geometric theorem discovery, which can give the complementary conditions such that the geometric statement becomes true or true on components. Some reducible geometric statements are given to illustrate our method.
关键词	Zero divisor True on components Grobner basis Geometric theorem proving Geometric theorem discovery
DOI	10.1007/s10817-016-9395-z
语种	英语
资助项目	National Nature Science Foundation of China[11301523] ; National Nature Science Foundation of China[11371356]
WOS研究方向	Computer Science
WOS类目	Computer Science, Artificial Intelligence
WOS记录号	WOS:000409976900002
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/26410
专题	系统科学研究所
通讯作者	Zhou, Jie
作者单位	1.Sci & Technol Commun Secur Lab, Chengdu 610041, Sichuan, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Inst Informat Engn, Beijing 100093, Peoples R China
推荐引用方式 GB/T 7714	Zhou, Jie,Wang, Dingkang,Sun, Yao. Automated Reducible Geometric Theorem Proving and Discovery by Grobner Basis Method[J]. JOURNAL OF AUTOMATED REASONING,2017,59(3):331-344.
APA	Zhou, Jie,Wang, Dingkang,&Sun, Yao.(2017).Automated Reducible Geometric Theorem Proving and Discovery by Grobner Basis Method.JOURNAL OF AUTOMATED REASONING,59(3),331-344.
MLA	Zhou, Jie,et al."Automated Reducible Geometric Theorem Proving and Discovery by Grobner Basis Method".JOURNAL OF AUTOMATED REASONING 59.3(2017):331-344.