If we transport the computation of a gcd from to we should be careful. For instance with
For we will take . For we will take .
Assume from now on that is a Unique Factorization Domain (UFD). This means that is an integral domain such that
The polynomial is primitive if . The primitive part of is the polynomial such that
In fact for computing gcds in (and more generally over ) the modular methods (to be described shortly) are much more efficient than going through and the Euclidean Algorithm.
The simplest approach would be
Marc Moreno Maza