The F5 algorithm in Buchberger’s style
The F5 algorithm in Buchberger’s style
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DOI：
10.1007/s11424-011-0218-3
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发表时间：
2010-06
影响因子：
2.1
通讯作者：
Yao Sun;Dingkang Wang
中科院分区：
文献类型：
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作者：
Yao Sun;Dingkang Wang
F5算法是Faugère在2002年提出的计算Gröbner基的著名算法。F5的原始版本是以编程代码的形式给出的，所以有点难以理解。本文将F5算法简化为Buchberger风格的F5 B算法，以便于理解和实现。为了描述F5 B，我们引入了F5-约简，它在约简后保持标记多项式的签名不变。还显示了F5和F5 B之间的等效性。最后，给出了F5算法的几种版本。
The famous F5 algorithm for computing Gröbner basis was presented by Faugère in 2002. The original version of F5 is given in programming codes, so it is a bit difficult to understand. In this paper, the F5 algorithm is simplified as F5B in a Buchberger’s style such that it is easy to understand and implement. In order to describe F5B, we introduce F5-reduction, which keeps the signature of labeled polynomials unchanged after reduction. The equivalence between F5 and F5B is also shown. At last, some versions of the F5 algorithm are illustrated.