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Automated short proof generation for projective geometric theorems with Cayley and bracket algebras - II. Conic geometry
Li, HB; Wu, YH
2003-11-01
发表期刊JOURNAL OF SYMBOLIC COMPUTATION
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
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
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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.
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