Constructing minimal telescopers for rational functions in three discrete variables

We present a new algorithm for constructing minimal tele-scop ers for rational functions in three discrete variables. This is the first discrete reduction-based algorithm that goes be-yond 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. (c) 2022 Elsevier Inc. All rights reserved.