Automated short proof generation for projective geometric theorems with Cayley and bracket algebras - II. Conic geometry

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	Automated short proof generation for projective geometric theorems with Cayley and bracket algebras - II. Conic geometry
	Li, HB ; Wu, YH
发表期刊	JOURNAL OF SYMBOLIC COMPUTATION
	2003-11-01
卷号	36 期号:5 页码:763-809
文章类型	Article
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.
关键词	Bracket Algebra Cayley Algebra Automated Theorem Proving Projective Conic Geometry
WOS标题词	Science & Technology ; Technology ; Physical Sciences
关键词[WOS]	INVARIANT-THEORY ; FACTORIZATION
收录类别	SCI
语种	英语
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Theory & Methods ; Mathematics, Applied
WOS记录号	WOS:000186484500004
引用统计	被引频次：5[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://ir.ia.ac.cn/handle/173211/9938
专题	09年以前成果
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.