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Automated short proof generation for projective geometric theorems with Cayley and bracket algebras - I. Incidence geometry
Li, HB; Wu, YH
Source PublicationJOURNAL OF SYMBOLIC COMPUTATION
2003-11-01
Volume36Issue:5Pages:717-762
SubtypeArticle
AbstractIn 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.
KeywordCayley Algebra Bracket Algebra Automated Theorem Proving Projective Incidence Geometry
WOS HeadingsScience & Technology ; Technology ; Physical Sciences
WOS KeywordINVARIANT-THEORY ; TRADITIONAL PROOFS ; FACTORIZATION ; POLYNOMIALS ; ALGORITHM
Indexed BySCI
Language英语
WOS Research AreaComputer Science ; Mathematics
WOS SubjectComputer Science, Theory & Methods ; Mathematics, Applied
WOS IDWOS:000186484500003
Citation statistics
Document Type期刊论文
Identifierhttp://ir.ia.ac.cn/handle/173211/9927
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
Recommended Citation
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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