author = {J. Ablinger and C. Schneider},
title = {{Solving linear difference equations with coefficients in rings with idempotent representations}},
language = {english},
abstract = {We introduce a general reduction strategy that enables one to search for solutions of parameterized linear difference equations in difference rings. Here we assume that the ring itself can be decomposed by a direct sum of integral domains (using idempotent elements) that enjoys certain technical features and that the coeicients of the difference equation are not degenerated. Using this mechanism we can reduce the problem to ind solutions in a ring (with zero- divisors) to search solutions in several copies of integral domains. Utilizing existing solvers in this integral domain setting, we obtain a general solver where the components of the linear difference equations and the solutions can be taken from difference rings that are built e.g., by $R\Pi\Sigma$-extensions over $\Pi\Sigma$-fields. This class of differ ence rings contains, e.g., nested sums and products, products over roots of unity and nested sums defined over such objects.},
number = {21-04},
year = {2021},
month = {February},
keywords = {linear difference equations, difference rings, idempotent elements},
length = {8},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}