A new proof for the correctness of the F5 algorithm
文献类型：期刊论文
| 作者 | Sun Yao; Wang DingKang |
| 刊名 | 中国科学:数学(英文版)
 |
| 出版日期 | 2013 |
| 卷号 | 56期号:4页码:745-756 |
| 关键词 | GROBNER BASES Grobner basis F5 F5B correctness of F5 |
| ISSN号 | 1674-7283 |
| 其他题名 | A new proof for the correctness of the F5 algorithm |
| 英文摘要 | 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. |
| 资助项目 | [National Key Basic Research Project of China] ; [National Natural Science Foundation of China] |
| 语种 | 中文 |
| CSCD记录号 | CSCD:4814855 |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/53495]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 作者单位 | 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. A new proof for the correctness of the F5 algorithm[J]. 中国科学:数学(英文版),2013,56(4):745-756. |
| APA | Sun Yao,&Wang DingKang.(2013).A new proof for the correctness of the F5 algorithm.中国科学:数学(英文版),56(4),745-756. |
| MLA | Sun Yao,et al."A new proof for the correctness of the F5 algorithm".中国科学:数学(英文版) 56.4(2013):745-756. |
入库方式： OAI收割
来源：数学与系统科学研究院
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