If I get a polynomial, say $u^5 + u^4 + u^2 + 1$, what is a simple and fast (by which I mean not to much to write) way to get the period of this term?
Should I first test whether the polynomial is primitive?
Edit By period I mean the smallest number $r$ such that $(u^r + 1) : p(u)$ can be done without a remainder. I should definitely mention that all this is done as a modulus calculation. So $u^5 + u^4 + u^3 + u^3 +u^2 +1 $ is exactly the same as the first example (i.e., there is no $2u^3$)