Attention, l'exposé aura lieu à l'École polytechnique, salle 108 au 1er étage du bâtiment Alan Turing.

Telescopers for Rational and Algebraic Functions via Residues.

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).