On the Summability Problem of Multivariate Rational Functions in the Mixed Case
Symbolic Computation
2026-02-04 v1
Abstract
Continuing previous work, this paper focuses on the summability problem of multivariate rational functions in the mixed case in which both shift and -shift operators can appear. Our summability criteria rely on three ingredients including orbital decompositions, Sato's isotropy groups, and difference transformations. This work settles the rational case of the long-term project aimed at developing algorithms for symbolic summation of multivariate functions.
Cite
@article{arxiv.2602.03289,
title = {On the Summability Problem of Multivariate Rational Functions in the Mixed Case},
author = {Shaoshi Chen and Lixin Du and Hanqian Fang and Yisen Wang},
journal= {arXiv preprint arXiv:2602.03289},
year = {2026}
}