采用Griffiths-Dwork方法的有理函数创造性望远镜法
Creative telescoping for rational functions using the Griffiths-Dwork method
AI总结：
本研究针对有理函数的创造性望远镜问题，提出了精确基础的Griffiths-Dwork算法版本，给出微分方程系数阶数与次数界，得到首个变量数单指数复杂度结果，且无需计算证书，经原型实现验证有效。
摘要：
创造性望远镜算法用于计算含参数的多重积分所满足的线性微分方程。我们针对有理函数的创造性望远镜问题，描述了Griffiths-Dwork方法的一种精确且基础的算法版本。该方法给出了微分方程系数的阶数与次数界，还得到了首个仅随变量个数呈单指数增长的复杂度结果。该算法的重要特性之一是无需计算证书（certificates）。一个原型实现验证了该方法的有效性。
英文摘要：
Creative telescoping algorithms compute linear differential equations satisfied by multiple integrals with parameters. We describe a precise and elementary algorithmic version of the Griffiths-Dwork method for the creative telescoping of rational functions. This leads to bounds on the order and degree of the coefficients of the differential equation, and to the first complexity result which is simply exponential in the number of variables. One of the important features of the algorithm is that it does not need to compute certificates. The approach is vindicated by a prototype implementation.
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