中国科学院机构知识库网格
Chinese Academy of Sciences Institutional Repositories Grid
Automated short proof generation for projective geometric theorems with Cayley and bracket algebras - II. Conic geometry

文献类型:期刊论文

作者Li, HB; Wu, YH
刊名JOURNAL OF SYMBOLIC COMPUTATION
出版日期2003-11-01
卷号36期号:5页码:763-809
关键词bracket algebra Cayley algebra automated theorem proving projective conic geometry
ISSN号0747-7171
DOI10.1016/S0747-7171(03)00066-X
英文摘要In this paper we study plane conic geometry, particularly different representations of geometric constructions and relations in plane conic geometry, with Cayley and bracket algebras. We propose three powerful simplification techniques for bracket computation involving conic points, and an algorithm for rational Cayley factorization in conic geometry. The factorization algorithm is not a general one, but works for all the examples tried so far. We establish a series of elimination rules for various geometric constructions based on the idea of bracket-oriented representation and elimination, and an algorithm for optimal representation of the conclusion in theorem proving. These techniques can be used in any applications involving brackets and conics. In theorem proving, our algorithm based on these techniques can produce extremely short proofs for difficult theorems in conic geometry. (C) 2003 Elsevier Ltd. All rights reserved.
WOS研究方向Computer Science ; Mathematics
语种英语
WOS记录号WOS:000186484500004
出版者ACADEMIC PRESS LTD ELSEVIER SCIENCE LTD
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/19121]  
专题中国科学院数学与系统科学研究院
通讯作者Li, HB
作者单位1.Chinese Acad Sci, Acad Math & Syst Sci, Math Mech Key Lab, Beijing 100080, Peoples R China
2.Chinese Acad Sci, Inst Automat, Natl Lab Pattern Recognit, Beijing 100080, Peoples R China
3.Univ Kiel, D-24098 Kiel, Germany
推荐引用方式
GB/T 7714
Li, HB,Wu, YH. Automated short proof generation for projective geometric theorems with Cayley and bracket algebras - II. Conic geometry[J]. JOURNAL OF SYMBOLIC COMPUTATION,2003,36(5):763-809.
APA Li, HB,&Wu, YH.(2003).Automated short proof generation for projective geometric theorems with Cayley and bracket algebras - II. Conic geometry.JOURNAL OF SYMBOLIC COMPUTATION,36(5),763-809.
MLA Li, HB,et al."Automated short proof generation for projective geometric theorems with Cayley and bracket algebras - II. Conic geometry".JOURNAL OF SYMBOLIC COMPUTATION 36.5(2003):763-809.

入库方式: OAI收割

来源:数学与系统科学研究院

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