 
Summary: On Some Decidable and Undecidable Problems Related to
QDifference Equations with Parameters
S. A. Abramov
Computing Centre of the Russian Academy of Sciences,
ul. Vavilova 40, Moscow, 119991
Russia
sergeyabramov@mail.ru
ABSTRACT
We consider linear qdifference equations with polynomial
coefficients depending on parameters. For the case when the
ground field is Q(q) we propose an algorithm recognizing
whether or not there exist numerical values of parameters for
which a given equation has a nonzero polynomial solution
(alternatively, a rationalfunction solution). We prove that
there exists no such algorithm if the parameter values are
polynomials or rational functions of q.
Categories and Subject Descriptors
I.1.2 [Symbolic And Algebraic Manipulation]: Algo
rithmsAlgebraic algorithms
General Terms
