Thursday 19 July 2012, 14h
Microsoft Research – Inria Joint Centre
Campus de l’Ecole polytechnique, Palaiseau
Bld Alan Turing, Salle Milner
Telescopers for Rational and Algebraic Functions via Residues.
Shaoshi Chen, North Carolina State University
We show that the problem of constructing telescopers for rational functions of m + 1 variables is equivalent to the problem of constructing telescopers for algebraic functions of m variables and we present a new algorithm to construct telescopers for algebraic functions of two variables. These considerations are based on analyzing the residues of the input. According to experiments, the resulting algorithm for rational functions of three variables is faster than known algorithms, at least in some examples of combinatorial interest. The algorithm for algebraic functions implies a new bound on the order of the telescopers.
This is a joint work with Manuel Kauers (RISC) and Michael F. Singer (NCSU).