Reduction-Based Creative Telescoping for Algebraic Functions

TL;DR

This paper introduces a new reduction-based algorithm for creative telescoping that constructs minimal telescopers for algebraic functions, extending previous methods to a broader class of functions.

Contribution

The paper develops a novel algorithm combining Trager's Hermite reduction and polynomial reduction for algebraic functions, advancing the computational techniques in creative telescoping.

Findings

Algorithm constructs minimal telescopers for algebraic functions.

Extends reduction-based creative telescoping methods to algebraic functions.

Improves efficiency and applicability of symbolic integration techniques.

Abstract

Continuing a series of articles in the past few years on creative telescoping using reductions, we develop a new algorithm to construct minimal telescopers for algebraic functions. This algorithm is based on Trager's Hermite reduction and on polynomial reduction, which was originally designed for hyperexponential functions and extended to the algebraic case in this paper.