Since the ring 
is Euclidean, Algorithm 3
can also be applied to polynomials. But, to obtain an efficient code,
some details have to be fixed. In first place, equality to 0 is
not so simple as in 
. You have to expand your polynomials to
their reduced normal form since e.g., 
answers 
. In second place, you gain efficiency when denominators
are avoided. Therefore, we take the content 
of the quotient 
i.e., the 
of the coefficients of , and use 
. The matricial version of the algorithm is given in Algorithm 6.
Exemplifying this algorithm with 
and 
, we obtain Figure 3.
