Rational summation of rational functions (Q1580085)

The author characterizes rational functions for which their indefinite sum is again a rational function. The rational summation problem has been studied by \textit{S. A. Abramov} [Zh. Vychisl. Mat. Mat. Fiz. 15, 1035-1039 (1975; Zbl 0326.65069)], \textit{P. Paule} [RISC-Linz Report Series No. 93-02 (1993) and J. Symb. Comput. 20, 235-268 (1995; Zbl 0854.68047)], \textit{R. Pirastu} [Algorithmen zur Summation rationaler Funktionen (in German). Diploma thesis, University of Erlangen-Nürnberg (1992)] and \textit{R. Pirastu} and \textit{V. Strehl} [J. Symb. Comput. 20, 617-635 (1995; Zbl 0851.68050)] who gave algorithms, based on either the Gosper-Petkovšek representation or the shift saturated representation of a rational function, to decide whether a rational function is rationally summable or not.