2023/07/14 by Hadrien Brochet, Bruno Salvy, Brochet, Hadrien +1 · 1 citation
Computer Science · Engineering · #Polynomial and algebraic computation #Advanced Numerical Analysis Techniques #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2307.07216
Creative telescoping is an algorithmic method initiated by Zeilberger to compute definite sums by synthesizing summands that telescope, called certificates. We describe a creative telescoping algorithm that computes telescopers for definite sums of D-finite functions as well as the associated certificates in a compact form. The algorithm relies on a discrete analogue of the generalized Hermite reduction, or equivalently, a generalization of the Abramov-Petkovšek reduction. We provide a Maple implementation with good timings on a variety of examples.