 
Summary: Rational Solutions of First Order Linear
qDi#erence Systems
S. A. Abramov #
Computer Center of
the Russian Academy of Science,
Vavilova 40, Moscow 117967, Russia
abramov@ccas.ru
sabramov@cs.msu.su
Abstract
We propose an algorithm to compute rational function solutions for a first order
system of linear qdi#erence equations with rational coe#cients. We make use of
the fact that qdi#erence equations bear similarity with di#erential equations at
the point 0 and with di#erence equations at other points. This allows combining
known algorithms for the di#erential and the di#erence cases.
1 Introduction
Let K be a computable field of characteristic zero, q # K a nonzero element which is not
a root of unity, and x transcendental over K.
A system of first order linear qdi#erence equations with rational coe#cients over the
field K is a system of the form :
p 1 (x)y 1 (qx) = a 11 (x)y 1 (x) + · · · + a 1m (x)y m (x) + b 1 (x)
