Proving geometric theorems by partitioned-parametric Grobner bases

CSpace > 系统科学研究所

	Proving geometric theorems by partitioned-parametric Grobner bases
	Chen, XF; Li, P; Lin, L; Wang, DK
	2006
发表期刊	AUTOMATED DEDUCTION IN GEOMETRY
ISSN	0302-9743
卷号	3763 页码:34-43
摘要	The notion of partitioned-parametric Grobner bases of a polynomial ideal under constraints is introduced and an algorithm for constructing partitioned-parametric Grobner bases is given; the correctness and the termination of the algorithm are proved. We also present a method based on computing partitioned-parametric Grobner bases for proving geometric theorems mechanically. By this method, besides proving the generic truth of a geometric theorem, we can give the necessary and sufficient conditions on the free parameters for the theorem to be true. An example for proving geometric theorems by the partitioned-parametric Gr6bner bases method is given.
语种	英语
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Artificial Intelligence ; Mathematics
WOS记录号	WOS:000235835500003
出版者	SPRINGER-VERLAG BERLIN
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/2681
专题	系统科学研究所
通讯作者	Chen, XF
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Chen, XF,Li, P,Lin, L,et al. Proving geometric theorems by partitioned-parametric Grobner bases[J]. AUTOMATED DEDUCTION IN GEOMETRY,2006,3763:34-43.
APA	Chen, XF,Li, P,Lin, L,&Wang, DK.(2006).Proving geometric theorems by partitioned-parametric Grobner bases.AUTOMATED DEDUCTION IN GEOMETRY,3763,34-43.
MLA	Chen, XF,et al."Proving geometric theorems by partitioned-parametric Grobner bases".AUTOMATED DEDUCTION IN GEOMETRY 3763(2006):34-43.