2012/01/10 by Shaoshi Chen, Manuel Kauers, Chen, Shaoshi +3 · 2 citations
Computer Science · Mathematics · #33F10 #68W30 #Algebraic Geometry (math.AG) #Coding theory and cryptography #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Computer and information sciences #FOS: Mathematics #I.1.2 #Polynomial and algebraic computation #Symbolic Computation (cs.SC) #acm:33F10 #acm:68W30 #cs.SC #math.AG #math.CO #msc:33F10 #msc:68W30
paper · pdf · doi:10.48550/arxiv.1201.1954
openalex publication_date 2012/01/10 · arxiv created 2012/01/11 · arxiv updated 2012/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the problem of constructing telescopers for functions of m variables is equivalent to the problem of constructing telescopers for algebraic functions of m -1 variables and present a new algorithm to construct telescopers for algebraic functions of two variables. These considerations are based on analyzing the residues of the input. According to experiments, the resulting algorithm for rational functions of three variables is faster than known algorithms, at least in some examples of combinatorial interest. The algorithm for algebraic functions implies a new bound on the order of the telescopers.