On the Summability Problem of Multivariate Rational Functions in the Mixed Case

2026/02/03 by Shaoshi Chen, Lixin Du, Hanqian Fang +1 · 1 voice
Computer Science · #cs.SC

paper · pdf · doi:10.1145/3815436.3815462

arxiv published 2026/02/03 · arxiv updated 2026/06/22

Abstract

Continuing previous work, this paper focuses on the summability problem of multivariate rational functions in the mixed case in which both shift and q-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.

Citations

• A Unified Reduction for Hypergeometric and q-Hypergeometric Creative Telescoping
• Symbolic Summation of Multivariate Rational Functions
• An Algorithmic Approach to the q-Summability Problem of Bivariate Rational Functions
• Some Open Problems related to Creative Telescoping
• An Algorithm for Deciding the Summability of Bivariate Rational Functions
• Testing Equivalence of Polynomials under Shifts
• On the Summability of Bivariate Rational Functions
• A Symbolic Summation Approach to Feynman Integral Calculus
• Differential Galois Theory of Linear Difference Equations
• A Telescoping method for Double Summations
• Integration of elementary functions

Discussions

• Shaoshi Chen, Lixin Du, Hanqian Fang, Yisen Wang: On the Summability Problem of Multivariate Rational Functions in the Mixed Case https://arxiv.org/abs/2602.03289 https://arxiv.org/pdf/2602.03289 http [bsky, 0 points, 0 comments]

Related

• Symbolic Summation of Multivariate Rational Functions
• An Algorithm for Deciding the Summability of Bivariate Rational Functions
• An Algorithmic Approach to the q-Summability Problem of Bivariate Rational Functions
• On the Summability of Bivariate Rational Functions
• Bivariate Extensions of Abramov's Algorithm for Rational Summation