@InProceedings{chen2018ACA, author="Chen, Shaoshi", editor="Schneider, Carsten and Zima, Eugene", title="Bivariate Extensions of Abramov's Algorithm for Rational Summation", booktitle="Advances in Computer Algebra", year="2018", publisher="Springer International Publishing", address="Cham", pages="93--104", abstract="Abramov's algorithm enables us to decide whether a univariate rational function can be written as a difference of another rational function, which has been a fundamental algorithm for rational summation. In 2014, Chen and Singer have generalized Abramov's algorithm to the case of rational functions in two (q-)discrete variables. In this paper we solve the remaining three mixed cases, which completes our recent project on bivariate extensions of Abramov's algorithm for rational summation.", isbn="978-3-319-73232-9" }