We present a new algorithm to compute minimal telescopers for rational functions in two discrete variables. As with recent reduction-based approaches, our algorithm has the important feature that the computation of a telescoper is independent of its certificate. In addition, our algorithm uses a compact representation of the certificate, which allows it to be easily manipulated and analyzed without knowing the precise expanded form. This representation hides potential expression swell until the final (and optional) expansion, which can be accomplished in time polynomial in the size of the expanded certificate. A complexity analysis, along with a Maple implementation, indicates that our algorithm has better theoretical and practical performance than the reduction-based approach in the rational case.

我们提出了一种新算法来计算两个离散变量中的有理函数的最小望远镜。与最近的基于缩减的方法一样，我们的算法具有一个重要特征，即望远镜的计算与其证书无关。此外，我们的算法使用证书的紧凑表示，这使得它可以在不知道精确扩展形式的情况下轻松操作和分析。这种表示隐藏了潜在的表达式膨胀，直到最终（和可选的）扩展，这可以在扩展证书大小的时间多项式中完成。复杂性分析以及 Maple 实现表明，我们的算法在合理情况下比基于约简的方法具有更好的理论和实践性能。