Can someone explain how to find inverses in truncated polynomial rings manually (i.e. on pen and paper)? As an example from the tutorial:
Example. Take $N=7$, $q=11$, $a=3+2X^2-3X^4+X^6$. The inverse of $a \bmod 11$ is $a^{-1}=-2+4X+2X^2+4X^3-4X^4+2X^5-2X^6$, since
$(3+2X^2-3X^4+X^6)*(-2+4^X+2X^2+4X^3-4X^4+2X^5-2X^6) \equiv -10+22X+22X^3-22X^6 \equiv 1 \mod 11$.
How to find $a^{-1} = -2+4X+2X^2+4X^3-4X^4+2X^5-2X^6$, manually, not using the pseudocode?
