Differential Rational Normal Forms and a Reduction Algorithm for Hyperexponential Functions

摘要

We describe differential rational normal forms of a rational function and their properties. Based on these normal forms, we present an algorithm which, given a hyperex-ponential function T(x), constructs two hyperexponential functions T_1(x) and T_2(x) such that T(x) = T′_1(x) + T_2(x) and T_2(x) is minimal in some sense. The algorithm can be used to accelerate the differential Gosper's algorithm and to compute right factors of the telescopers.