 
Summary: Factorization of Polynomials and GCD
Computations for Finding Universal
Denominators
S.A. Abramov1
, A. Gheffar2
, and D.E. Khmelnov1
1
Computing Centre of the Russian Academy of Sciences, Vavilova,
40, Moscow 119991, GSP1 Russia
sergeyabramov@mail.ru, dennis khmelnov@mail.ru
2
Institute XLIM, Universit´e de Limoges, CNRS, 123, Av. A. Thomas,
87060 Limoges cedex, France
f gheffar@yahoo.fr
Abstract. We discuss the algorithms which, given a linear difference
equation with rational function coefficients over a field k of characteristic
0, compute a polynomial U(x) k[x] (a universal denominator) such
that the denominator of each of rational solutions (if exist) of the given
equation divides U(x). We consider two types of such algorithms. One
of them is based on constructing a set of irreducible polynomials that
