关于F5算法的准则
On The Criteria Of The F5 Algorithm
摘要：
Faugere的F5算法是已知的计算Grobner基的最快算法之一。到目前为止，只有F5准则得到了证明，而第二个强有力的准则，重写准则，直到现在还没有得到很好的理解。我们给出了一个证明，F5标准和重写标准显示他们的连接syzygies，即之间的关系的S-多项式的算法进行调查。使用的例子Grobner基础计算Faugere的F5文件中所述，我们展示了如何标准的工作，并讨论了改进的F5标准的可能性。最后介绍了F5的一个SINGULAR实现。
英文摘要：
Faugere's F5 algorithm is one of the fastest known algorithms for the computation of Grobner bases. So far only the F5 Criterion is proved, whereas the second powerful criterion, the Rewritten Criterion, is not understood very well until now. We give a proof of both, the F5 Criterion and the Rewritten Criterion showing their connection to syzygies, i.e. the relations between the S-Polynomials to be investigated by the algorithm. Using the example of a Grobner basis computation stated in Faugere's F5 paper we show how the criteria work, and discuss the possibility of improving the F5 Criterion. An introduction to a SINGULAR implementation of F5 is given in the end.
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。
