Gcd Algorithms in $\bf k$[x₁,..., x_n] where $\bf k$ is a field

For n = 2 use the previous section, since $\bf k$[x₁] is an Euclidean domain. Of course this requires some additional explanations. For n > 2 use evaluation-interpolation in order to reduce to the case n = 2. Again, some details would need to be added.