🤖 AI Summary
本文解决了F4算法中行阶梯形计算的瓶颈问题，通过提供概率性算法错误概率的界限，并提出一种拉斯维加斯变体，实验表明在某些情况下优于确定性F4。
📝 Abstract
The computation of row echelon form is one of the main bottlenecks in the F4 algorithm. Several state of the art implementations use a probabilistic algorithm attributed to Monagan, Pearce, and Steel to accelerate this computation. Despite this, no bound on the probability that the algorithm returns an incorrect result appears to be available. In this paper, we provide such a bound. Furthermore, building on this result, we propose a Las-Vegas variant of the F4 algorithm and show experimentally that it can outperform deterministic F4 on some classical examples.