2019/01/27 by Shaoshi Chen, Chen, Shaoshi, Lixin Du +5 · 1 citation
Computer Science · Mathematics · #33F10 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Polynomial and algebraic computation #Symbolic Computation (cs.SC) #cs.SC #math.CO #msc:33F10 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1901.09377
30 pages
openalex publication_date 2019/01/27 · arxiv created 2020/02/17 · arxiv updated 2020/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Zeilberger's method of creative telescoping is crucial for the computer-generated proofs of combinatorial and special-function identities. Telescopers are linear differential or (q-)recurrence operators computed by algorithms for creative telescoping. For a given class of inputs, when telescopers exist and how to construct telescopers efficiently if they exist are two fundamental problems related to creative telescoping. In this paper, we solve the existence problem of telescopers for rational functions in three variables including 18 cases. We reduce the existence problem from the trivariate case to the bivariate case and some related problems. The existence criteria given in this paper enable us to determine the termination of algorithms for creative telescoping with trivariate rational inputs.