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Automated short proof generation for projective geometric theorems with Cayley and bracket algebras - I. Incidence geometry
Li, HB; Wu, YH
2003-11-01
发表期刊JOURNAL OF SYMBOLIC COMPUTATION
卷号36期号:5页码:717-762
文章类型Article
摘要In this paper we establish the Cayley expansion theory on factored and shortest expansions of typical Cayley expressions in two- and three-dimensional projective geometry. We set up a group of Cayley factorization formulae based on the classification of Cayley expansions. We continue to establish three powerful simplification techniques in bracket computation. On top of the Cayley expansions and simplifications, together with a set of elimination rules, we design an algorithm that can produce extremely short proofs in two- and three-dimensional projective geometry. The techniques developed here can be immediately applied to other symbolic computation tasks involving brackets. (C) 2003 Elsevier Ltd. All rights reserved.
关键词Cayley Algebra Bracket Algebra Automated Theorem Proving Projective Incidence Geometry
WOS标题词Science & Technology ; Technology ; Physical Sciences
关键词[WOS]INVARIANT-THEORY ; TRADITIONAL PROOFS ; FACTORIZATION ; POLYNOMIALS ; ALGORITHM
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:000186484500003
引用统计
文献类型期刊论文
条目标识符http://ir.ia.ac.cn/handle/173211/9927
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
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 - I. Incidence geometry[J]. JOURNAL OF SYMBOLIC COMPUTATION,2003,36(5):717-762.
APA Li, HB,&Wu, YH.(2003).Automated short proof generation for projective geometric theorems with Cayley and bracket algebras - I. Incidence geometry.JOURNAL OF SYMBOLIC COMPUTATION,36(5),717-762.
MLA Li, HB,et al."Automated short proof generation for projective geometric theorems with Cayley and bracket algebras - I. Incidence geometry".JOURNAL OF SYMBOLIC COMPUTATION 36.5(2003):717-762.
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