Affine bracket algebra theory and algorithms and their applications in mechanical theorem proving

doi:10.1007/s11425-007-0076-6

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	Affine bracket algebra theory and algorithms and their applications in mechanical theorem proving
	Zhang, Ning ; Li, Hong-bo
	2007-07-01
发表期刊	SCIENCE IN CHINA SERIES A-MATHEMATICS
ISSN	1006-9283
卷号	50 期号:7 页码:941-950
摘要	This paper discusses two problems: one is some important theories and algorithms of affine bracket algebra; the other is about their applications in mechanical theorem proving. First we give some efficient algorithms including the boundary expanding algorithm which is a key feature in application. We analyze the characteristics of the boundary operator and this is the base for the implementation of the system. We also give some new theories or methods about the exact division, the representations and structure of affine geometry and so on. In practice, we implement the mechanical auto-proving system in Maple 10 based on the above algorithms and theories. Also we test about more than 100 examples and compare the results with the methods before.
关键词	mechanical theorem proving geometric invariance bracket algebra affine geometry affine bracket algebra
DOI	10.1007/s11425-007-0076-6
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000248202100003
出版者	SCIENCE CHINA PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/4992
专题	系统科学研究所
通讯作者	Zhang, Ning
作者单位	1.Cent Univ Finance & Econ, CIAS, Beijing 100081, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Ning,Li, Hong-bo. Affine bracket algebra theory and algorithms and their applications in mechanical theorem proving[J]. SCIENCE IN CHINA SERIES A-MATHEMATICS,2007,50(7):941-950.
APA	Zhang, Ning,&Li, Hong-bo.(2007).Affine bracket algebra theory and algorithms and their applications in mechanical theorem proving.SCIENCE IN CHINA SERIES A-MATHEMATICS,50(7),941-950.
MLA	Zhang, Ning,et al."Affine bracket algebra theory and algorithms and their applications in mechanical theorem proving".SCIENCE IN CHINA SERIES A-MATHEMATICS 50.7(2007):941-950.