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Sun Yao1; Wang Dingkang2
Source Publicationsciencechinamathematics
AbstractIn 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.
Funding Project[National Key Basic Research Project of China] ; [National Natural Science Foundation of China]
Document Type期刊论文
Recommended Citation
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.
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