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Indefinite sums of rational functions # S.A.Abramov
 

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)

  

Source: Abramov, Sergei A. - Dorodnicyn Computing Centre of the Russian Academy of Sciences

 

Collections: Mathematics; Computer Technologies and Information Sciences