In this paper we state and explain techniques useful for the computation of strong Gröbner and standard bases over Euclidean domains: First we investigate several strategies for creating the pair set using an idea by Lichtblau. Then we explain methods for avoiding coefficient growth using syzygies. We give an in-depth discussion on normal form computation resp. a generalized reduction process with many optimizations to further avoid large coefficients. These are combined with methods to reach GCD-polynomials at an earlier stage of the computation. Based on various examples we show that our new implementation in the computer algebra system Singular is, in general, more efficient than other known implementations.

在本文中，我们陈述并解释了对计算欧几里得域上的强Gröbner和标准碱基有用的技术：首先，我们研究使用Lichtblau的思想创建对对的几种策略。然后，我们解释了使用syzygies避免系数增长的方法。我们对正态计算的响应进行了深入的讨论。具有许多优化的广义归约过程，可以进一步避免大系数。这些方法与在计算的较早阶段达到GCD多项式的方法结合在一起。根据各种示例，我们表明，计算机代数系统Singular中的新实现通常比其他已知实现更有效。