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Difference Ring Algorithms for Symbolic Summation and Challenging Applications
Carsten Schneider, RISC-Linz (Austria)
Date & time: Thursday, 16 September 2021 at 5:00PM - 6:00PM
Abstract: A major breakthrough in symbolic summation was Doron Zeilberger's creative telescoping method to compute linear recurrences of definite hypergeometric sums. In this talk I will illustrate the algorithmic framework in the setting of difference rings in which one can extend Z's method for summands that are built by indefinite nested sums and products. In combination with a sophisticated recurrence solver one obtains a rather general machinery to simplify big classes of definite multi-sums to expressions in terms of indefinite nested sums and products. The underlying difference ring algorithms implemented in the summation package Sigma will be illustrated by non-trivial applications coming, e.g., from combinatorics and particle physics.
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