A Polynomial Time Algorithm for Calculating Fourier-Dedekind Sums - Xin, Guoce; Xu, Xinyu (Experimental mathematics, 2025)
We solve an open problem proposed in the book "Computing the continuous discretely" written by Matthias Beck and Sinai Robins. That is, we provide a practical polynomial time algorithm for calculating Fourier-Dedekind sums. The algorithm is simple modular Barvinok's simplicial cone decomposition. It can be easily adapted into De Leora et al.'s LattE package, which gives a nice implementation of Barvinok's polynomial time algorithm.