A Fast Approach to Creative Telescoping

TL;DR

This paper presents a new, faster method for computing creative telescoping relations in differential-difference operator algebras, significantly improving efficiency over existing techniques.

Contribution

It introduces an ansatz-based approach that explicitly incorporates denominators, along with implementation strategies that enhance computational speed.

Findings

Method outperforms existing approaches by a large margin

Implementation demonstrates significant speed improvements

Applicable to a range of examples in creative telescoping

Abstract

In this note we reinvestigate the task of computing creative telescoping relations in differential-difference operator algebras. Our approach is based on an ansatz that explicitly includes the denominators of the delta parts. We contribute several ideas of how to make an implementation of this approach reasonably fast and provide such an implementation. A selection of examples shows that it can be superior to existing methods by a large factor.