Polynomial greatest common divisor algorithm

Question

I look for an algorithm for Polynomial greatest common divisor.
I saw this at Wikipedia but I didn't understand where is the algorithm.

If you have other source for this algorithm, or you can write to me, or tell where I can find it at Wikipedia (at the link)...

Thank you!

Answer 1

to find gcd($f,g$) with $deg(g) < deg(f)$, write $f = g q_1 + r_1$ with $deg(r_1) < deg(g)$; then \begin{equation*} gcd(f,g) = gcd(r_1,g) \end{equation*}

Again, write $g = q_2 r_1 + r_2$ with $deg(r_2) < deg(r_1)$; then \begin{equation*} gcd(f,g) = gcd(r_1,g) = gcd(r_1,r_2) \end{equation*}

Continue this process until you get $gcd(r_n,0)$, which in this case you will have $gcd(r_n,0) = r_n$, and so $gcd(f,g) = r_n$.