# Constructing minimal telescopers for rational functions in three discrete variables

## TL;DR

This paper introduces a novel, efficient algorithm for constructing minimal telescopers for rational functions in three discrete variables, advancing beyond previous bivariate methods and avoiding costly certificate computations.

## Contribution

It presents the first discrete reduction-based algorithm for three-variable rational functions with guaranteed termination and improved efficiency.

## Key findings

- Algorithm successfully constructs minimal telescopers in three variables
- Avoids costly certificate computations
- Demonstrates efficiency through computational experiments

## Abstract

We present a new algorithm for constructing minimal telescopers for rational functions in three discrete variables. This is the first discrete reduction-based algorithm that goes beyond 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.