We present a new algorithm for constructing minimal telescopers for rational functions in three discrete variables. This is the first discrete reduction-based algorithm that goes beyond the bivariate case. The termination of the algorithm is guaranteed by a known existence criterion of telescopers. Our approach has the important feature that it avoids the potentially costly computation of certificates. Computational experiments are also provided so as to illustrate the efficiency of our approach.
翻译:我们提出了一个新的算法,用于在三个离散变量中为理性功能构建最小望远镜。 这是第一种离散的递减算法, 它超越了两变法。 算法的终止由已知的望远镜存在标准来保证。 我们的方法有一个重要特征, 它避免了计算证书的潜在成本。 还提供了计算实验, 以说明我们方法的效率。