In this paper we study the generic setting of the modular GCD algorithm. We develop the algorithm for multivariate polynomials over Euclidean domains which have a special kind of remainder function. Details for the parameterization and generic Maple code are given. Applying this generic algorithm to a GCD problem in Z/(p)[t][x] where p is small yields an improved asymptotic performance over the usual approach, and a very practical algorithm for polynomials over small finite fields.
Erich Kaltofen, Michael B. Monagan