Differential rational normal forms and a reduction algorithm for hyperexponential func

Authors:
Keith Geddes;Ha Le;Ziming Li
Affiliations:
University of Waterloo, Waterloo, ON, Canada;INRIA Rocquencourt, Cedex, France;Chinese Academy of Sciences, Beijing, China
Venue:
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Year:
2004

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Abstract

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 hyperexponential 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.