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Summary: On Some Decidable and Undecidable Problems Related to
Q-Difference 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 q-difference 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 non-zero polynomial solution
(alternatively, a rational-function 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-
rithms--Algebraic algorithms
General Terms
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