 
Summary: EGeliminations #
Sergei 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 put linear recurrent systems in a form which is convenient for
using the systems to search for polynomial, powerseries, Laurentseries, and other types of solutions
of various linear functional systems (di#erential, di#erence and qdi#erence). Some algorithms to
search for solutions of functional systems are described. None of the proposed algorithms requires
preliminary uncoupling of linear systems.
1 Introduction
Linear recurrences with variable coe#cients are of interest for combinatorics and numeric computation.
Additionally they give a useful auxiliary tool for constructing solutions of linear functional equations
(di#erential, di#erence and qdi#erence) in the form of polynomials, power and Laurent series, rational
functions, and so on [4, 8, 7].
Linear recurrent systems are more general and universal instruments. But working with recurrent
systems is more complicated than working with scalar recurrences. When we consider a recurrence
p l (n)z n+l + p l1 (n)z n+l1 + · · · + p t (n)z n+t = b n
with an unknown sequence z = {zn } then in many situations (e.g., if the coe#cients of this recurrence
