Automated short proof generation for projective geometric theorems with Cayley and bracket algebras - I. Incidence geometry
文献类型：期刊论文
| 作者 | Li, HB; Wu, YH
|
| 刊名 | JOURNAL OF SYMBOLIC COMPUTATION
 |
| 出版日期 | 2003-11-01 |
| 卷号 | 36期号:5页码:717-762 |
| 关键词 | Cayley algebra bracket algebra automated theorem proving projective incidence geometry |
| 英文摘要 | 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. |
| WOS标题词 | Science & Technology ; Technology ; Physical Sciences |
| 类目[WOS] | Computer Science, Theory & Methods ; Mathematics, Applied |
| 研究领域[WOS] | Computer Science ; Mathematics |
| 关键词[WOS] | INVARIANT-THEORY ; TRADITIONAL PROOFS ; FACTORIZATION ; POLYNOMIALS ; ALGORITHM |
| 收录类别 | SCI |
| 语种 | 英语 |
| WOS记录号 | WOS:000186484500003 |
| 公开日期 | 2015-12-24 |
| 源URL | [http://ir.ia.ac.cn/handle/173211/9927]  |
| 专题 | 自动化研究所_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. |
入库方式： OAI收割
来源：自动化研究所
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