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Automated Reducible Geometric Theorem Proving and Discovery by Grobner Basis Method

文献类型：期刊论文

作者Zhou, Jie1; Wang, Dingkang2; Sun, Yao3
刊名JOURNAL OF AUTOMATED REASONING
出版日期2017-10-01
卷号59期号:3页码:331-344
关键词Zero divisor True on components Grobner basis Geometric theorem proving Geometric theorem discovery
ISSN号0168-7433
DOI10.1007/s10817-016-9395-z
英文摘要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.
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
语种英语
WOS记录号WOS:000409976900002
出版者SPRINGER
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/26409]  
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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