Automated short proof generation for projective geometric theorems with Cayley and bracket algebras - II. Conic 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:763-809 |
| 关键词 | bracket algebra Cayley algebra automated theorem proving projective conic geometry |
| ISSN号 | 0747-7171 |
| DOI | 10.1016/S0747-7171(03)00066-X |
| 英文摘要 | In 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. |
| WOS研究方向 | Computer Science ; Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000186484500004 |
| 出版者 | ACADEMIC PRESS LTD ELSEVIER SCIENCE LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/19121]  |
| 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 3.Univ Kiel, D-24098 Kiel, Germany |
| 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 - 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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