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Rational Solutions of Linear Difference Equations Revisited Sergei Abramov ) 1
 

Summary: Rational Solutions of Linear Difference Equations Revisited
Sergei Abramov ) 1
, Amel Gheffar )
, Denis Khmelnov ) 1
) Computing Centre of the Russian Academy of Sciences
Vavilova, 40, Moscow 119991, GSP-1, Russia
sergeyabramov@mail.ru, dennis khmelnov@mail.ru
) XLIM, Universit´e de Limoges, CNRS
123, Av. A. Thomas, 87060 Limoges cedex
f gheffar@yahoo.fr
Abstract. We discuss algorithms that are currently used for computing ra-
tional solutions of linear difference systems (or of scalar equations) with poly-
nomial coefficients. A complexity analysis and a time comparison of the algo-
rithms implemented in Maple are presented.
1 Introduction
This paper is a summary of authors' results that have been published in [16, 7, 15, 8].
We revisit a problem of the search for rational solutions of a linear difference equation
with polynomial coefficients. Rational solutions may be a building block for other
types of solutions, and more general, such algorithms may be a part of various
computer algebra algorithms (see [22, 9, 10, 18], etc.). Investigations of new ways

  

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

 

Collections: Mathematics; Computer Technologies and Information Sciences