 
Summary: Indefinite sums of rational functions #
S.A.Abramov
Computer Center of the Russian Academy of Science
Vavilova 40, Moscow 117967, Russia
abramov@sms.ccas.msk.su
Abstract
We propose a new algorithm for indefinite rational summa
tion which, given a rational function F (x), extracts a ratio
nal part R(x) from the indefinite sum of F (x):
# F (x) = R(x) + # H(x).
If H(x) is not equal to 0 then the denominator of this ratio
nal function has the lowest possible degree. We then solve
the same probleme in the qdi#erence case.
1 The decomposition problem
We discuss here the problem of indefinite summation of ra
tional functions. This problem is equivalent to the problem
of solving the di#erence equation
y(x + 1)  y(x) = F (x) (1)
where F (x) is a rational function over a field K of charac
teristic 0. The decomposition problem is to find whether (1)
