Big O

How to multiply polynomials in Θ(n log n) time

The information in this post is taken from the sources listed in the Sources section at the end of it. If you don’t care about understanding the algorithm and need an implementation now, skip to the Implementation subsection. Why? Why would anyone want to multiply polynomials in $\Theta (n \log n)$ instead of the naive $\Theta(n^2)$ time? Sometimes happens. I did when I got confronted with the UVa Online Judge 12879 Golf Bot problem.