Why is polynomial convolution equivalent to multiplication in $F[x]/(x^n-1)$?
From this, I still can not understand how to get this $$ \begin{align} &f*g +(x^n-1)\sum_{k=0}^{n-1}\sum_{i+j=k+n}f_ig_jx^k \end{align} $$
from $$ \begin{align} \sum_{k=0}^{n-1}\left(\sum_{i+j=k}f_ig_j+\sum_{i+j=k+n}f_ig_jx^n\right)x^k\\ \end{align} $$
Thanks for answers.
