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 |
| ISSN号 | 0747-7171 |
| DOI | 10.1016/S0747-7171(03)00067-1 |
| 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研究方向 | Computer Science ; Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000186484500003 |
| 出版者 | ACADEMIC PRESS LTD ELSEVIER SCIENCE LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/18965]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Li, HB |
| 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：数学与系统科学研究院
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