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Séminaire Lotharingien de Combinatoire, B31b (1993), 7pp.

[Formerly: Publ. I.R.M.A. Strasbourg, 1994/021, p. 95-101.]

# Roberto Pirastu

# A Note on the Minimality Problem in Indefinite Summation of
Rational Functions

**Abstract.**
Given a rational function *f*,
the problem of indefinite summation is to find rational functions *h*
and *r* such that *f*(*n*) = *h*(*n*+1) -
*h*(*n*) + *r*(*n*). We are interested in solutions
(*h,r*) with both *h* and *r* of minimal degree in the
denominator. Our observations prove that the modification of Abramov's
algorithm proposed in ("*Algorithmen zur Summation rationaler
Funktionen*," Diploma Thesis, Univ. Erlangen-Nürnberg,
1992;
"*Algorithms for indefinite summation of rational functions in
Maple*," The Maple Techn. Newsletter **2** (1995))
produces such *minimal* solutions for a certain class of
rational summands.

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