I am looking for the fastest algorithm to calculate the $$C^n$$ where the $C$ is some algebraic constant.
For example it can be $$C=\frac{\sqrt3-1}{2}$$ or one of the root of $$x^5+x^2-1=0$$
If $$C=2$$ the algorithm is very simple and it has complexity $O(\ln n)$. The same is for any other natural number I assume.