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Automated Reducible Geometric Theorem Proving and Discovery by Grobner Basis Method
Zhou, Jie1; Wang, Dingkang2; Sun, Yao3
2017-10-01
Source PublicationJOURNAL OF AUTOMATED REASONING
ISSN0168-7433
Volume59Issue:3Pages:331-344
AbstractIn 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.
KeywordZero divisor True on components Grobner basis Geometric theorem proving Geometric theorem discovery
DOI10.1007/s10817-016-9395-z
Language英语
Funding ProjectNational Nature Science Foundation of China[11301523] ; National Nature Science Foundation of China[11371356]
WOS Research AreaComputer Science
WOS SubjectComputer Science, Artificial Intelligence
WOS IDWOS:000409976900002
PublisherSPRINGER
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/26410
Collection系统科学研究所
Corresponding AuthorZhou, Jie
Affiliation1.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
Recommended Citation
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.
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