计算合点的改进算法
Refined Algorithms to Compute Syzygies
摘要：
基于Schreyer算法（Schreyer，1980，1991; Berkesch and Schreyer，2014），我们提出了两种用于计算合点的改进算法。第一种算法称为LiftHybrid，其主要思想如下：首先，我们可以在计算过程中忽略某些对结果没有贡献的模块元素。这些项称为“低阶项”，见定义4.2。其次，我们不需要在计算过程中对这些模元素的其余项进行排序。这大大减少了算术运算的单项比较次数。对于第二个算法，称为LiftTree，我们额外缓存了一些部分结果，并在剩余的步骤中重用它们。
英文摘要：
Based on Schreyer's algorithm (Schreyer, 1980, 1991; Berkesch and Schreyer, 2014), we present two refined algorithms for the computation of syzygies. The two main ideas of the first algorithm, called LiftHybrid, are the following: First, we may leave out certain terms of module elements during the computation which do not contribute to the result. These terms are called "lower order terms", see Definition 4.2. Second, we do not need to order the remaining terms of these module elements during the computation. This significantly reduces the number of monomial comparisons for the arithmetic operations. For the second algorithm, called LiftTree, we additionally cache some partial results and reuse them at the remaining steps.
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