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Automated short proof generation for projective geometric theorems with Cayley and bracket algebras - II. Conic geometry
Li, HB; Wu, YH
Source PublicationJOURNAL OF SYMBOLIC COMPUTATION
2003-11-01
Volume36Issue:5Pages:763-809
SubtypeArticle
AbstractIn 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.
KeywordBracket Algebra Cayley Algebra Automated Theorem Proving Projective Conic Geometry
WOS HeadingsScience & Technology ; Technology ; Physical Sciences
WOS KeywordINVARIANT-THEORY ; FACTORIZATION
Indexed BySCI
Language英语
WOS Research AreaComputer Science ; Mathematics
WOS SubjectComputer Science, Theory & Methods ; Mathematics, Applied
WOS IDWOS:000186484500004
Citation statistics
Cited Times:4[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.ia.ac.cn/handle/173211/9938
Collection09年以前成果
Affiliation1.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
Recommended Citation
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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