anewproofforthecorrectnessofthef5algorithm

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	anewproofforthecorrectnessofthef5algorithm
	Sun Yao 1; Wang Dingkang2
	2013-01-01
发表期刊	sciencechinamathematics
ISSN	1674-7283
卷号	56 期号:4 页码:745
摘要	In 2002, FaugSre presented the famous F5 algorithm for computing Grobner basis where two criteria, syzygy criterion and rewritten criterion, were proposed to avoid redundant computations. He proved the correctness of the syzygy criterion, but the proof for the correctness of the rewritten criterion was left. Since then, F5 has been studied extensively. Some proofs for the correctness of F5 were proposed, but these proofs are valid only under some extra assumptions. In this paper, we give a proof for the correctness of F5B, an equivalent version of F5 in Buchberger's style. The proof is valid for both homogeneous and non-homogeneous polynomial systems. Since this proof does not depend on the computing order of the S-pairs, any strategy of selecting S-pairs could be used in F5B or F5. Furthermore, we propose a natural and non-incremental variant of F5 where two revised criteria can be used to remove almost all redundant S-pairs.
语种	英语
资助项目	[National Key Basic Research Project of China] ; [National Natural Science Foundation of China]
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/44782
专题	系统科学研究所
作者单位	1.中国科学院信息工程研究所 2.中国科学院数学与系统科学研究院
推荐引用方式 GB/T 7714	Sun Yao,Wang Dingkang. anewproofforthecorrectnessofthef5algorithm[J]. sciencechinamathematics,2013,56(4):745.
APA	Sun Yao,&Wang Dingkang.(2013).anewproofforthecorrectnessofthef5algorithm.sciencechinamathematics,56(4),745.
MLA	Sun Yao,et al."anewproofforthecorrectnessofthef5algorithm".sciencechinamathematics 56.4(2013):745.