Telescopers for a function are linear differential (resp. difference) operators annihilated by the definite integral (resp. definite sum) of this function. They play a key role in Wilf-Zeilberger theory and algorithms for computing them have been extensively studied in the past thirty years. In this paper, we introduce the notion of telescopers for differential forms with $D$-finite function coefficients. These telescopers appear in several areas of mathematics, for instance parametrized differential Galois theory and mirror symmetry. We give a sufficient and necessary condition for the existence of telescopers for a differential form and describe a method to compute them if they exist. Algorithms for verifying this condition are also given.
翻译：函数的望远镜是线性差( resp. difference) 操作员, 被该函数的确定整体( resp. de定数) 消灭。 他们在Wilf- Zeilberger理论和计算这些函数的算法中发挥了关键作用。 在过去三十年中,我们广泛研究了这些函数的计算方法。 在本文中, 我们引入了以$D$- finite 函数系数表示不同形式的望远镜员的概念。 这些望远镜出现在数学的若干领域, 例如, 等同的Galois 理论和镜面对称。 我们给望远镜的存在提供了足够和必要的条件, 以便有差异的形式存在, 并描述一种计算方法 。 也给出了用于验证该条件的参数 。
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