临界对最小集的有效计算
Efficiently Computing Minimal Sets of Critical Pairs
摘要：
在使用Buchberger算法计算Gr 'obner基时，提高效率的一个关键问题是提出尽可能避免不必要的临界对的技术。一个好的解决方案是避免_all_ non-minimal临界对，因此只处理临界合朔生成的模块的生成元的_minimal_ set。在本文中，我们将展示如何获得所需的解决方案，在同质的情况下，同时保持与经典的实现相同的效率。从而得到一个新的优化Buchberger算法。
英文摘要：
In the computation of a Gr"obner basis using Buchberger's algorithm, a key issue for improving the efficiency is to produce techniques for avoiding as many unnecessary critical pairs as possible. A good solution would be to avoid _all_ non-minimal critical pairs, and hence to process only a_minimal_ set of generators of the module generated by the critical syzygies. In this paper we show how to obtain that desired solution in the homogeneous case while retaining the same efficiency as with the classical implementation. As a consequence, we get a new Optimized Buchberger Algorithm.
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。
