Lazy Hermite Reduction and Creative Telescoping for Algebraic Functions

TL;DR

This paper enhances lazy Hermite reduction by combining it with polynomial reduction to improve symbolic integration of algebraic functions, and develops a telescoping algorithm for functions of two variables.

Contribution

It introduces a sharpened reduction method that efficiently decomposes algebraic functions and applies it to create a telescoping algorithm for bivariate algebraic functions.

Findings

Improved decomposition of algebraic functions

Efficient telescoping algorithm for two-variable functions

Enhanced symbolic integration techniques

Abstract

Bronstein's lazy Hermite reduction is a symbolic integration technique that reduces algebraic functions to integrands with only simple poles without the prior computation of an integral basis. We sharpen the lazy Hermite reduction by combining it with the polynomial reduction to solve the decomposition problem of algebraic functions. The sharpened reduction is then used to design a reduction-based telescoping algorithm for algebraic functions in two variables.