An Algorithmic Approach to the $q$-Summability Problem of Bivariate Rational Functions

TL;DR

This paper extends previous work on summability of bivariate rational functions by developing a simplified algorithm for the $q$-case, enhancing computational methods in this area.

Contribution

The paper introduces a simplified and adapted algorithm for the $q$-summability problem of bivariate rational functions, building on prior solutions.

Findings

Developed a simplified algorithm for $q$-summability.

Extended previous summability algorithms to the $q$-case.

Enhanced computational efficiency for summability problems.

Abstract

In 2014, Chen and Singer solved the summability problem of bivariate rational functions. Later an algorithmic proof was presented by Hou and the author. In this paper, the algorithm will be simplified and adapted to the $q$-case.