Gcd Algorithms in ${\bf k}[x_1, \ldots , x_n]$ where ${\bf k}$ is a field

For $n=2$ use the previous section, since ${\bf k}[x_1]$ 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.