修订了F5标准
The F5 Criterion revised
摘要：
这项工作的目的是推广Faugere的“F5”算法背后的理论的一部分。这是已知计算多项式理想I的Groebner基的最快算法之一，该多项式理想I由多项式f_{1}，.，f_{m}。一个主要的原因是Faugere所谓的算法的“新”准则，我们称之为“F5准则”;它提供了一个充分条件的一组多项式G是Groebner基础。然而，F5算法很难掌握，并且关于其终止存在未解决的问题。本文引入了一些新的概念，把准则放在一个更一般的设置：S-Groebner基和本原S-不可约多项式。我们使用这些提出了一个新的，简单的算法的基础上修订的F5标准。新概念还使我们能够消除各种限制，例如证明终止而不需要f_{1}，.，f_{m}是正则序列。
英文摘要：
The purpose of this work is to generalize part of the theory behind Faugere's "F5" algorithm. This is one of the fastest known algorithms to compute a Groebner basis of a polynomial ideal I generated by polynomials f_{1},...,f_{m}. A major reason for this is what Faugere called the algorithm's "new" criterion, and we call "the F5 criterion"; it provides a sufficient condition for a set of polynomials G to be a Groebner basis. However, the F5 algorithm is difficult to grasp, and there are unresolved questions regarding its termination. This paper introduces some new concepts that place the criterion in a more general setting: S-Groebner bases and primitive S-irreducible polynomials. We use these to propose a new, simple algorithm based on a revised F5 criterion. The new concepts also enable us to remove various restrictions, such as proving termination without the requirement that f_{1},...,f_{m} be a regular sequence.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
