I've been trying to understand Schools-algorithm. It's nicely described by http://www-users.math.umn.edu/~musiker/schoof.pdf but I still don't understand his statement on page 7, where he is saying the following:
We will soon use the following fact: If $x′ = x_{\overline{t}}^q$ for one point $P$ in $E[l]\setminus\{P_{\infty}\}$, then $\overline{t}$ satisfies \begin{equation*} \tau^2(P)\ominus \overline{t} \tau(P) \oplus qP = P_{\infty} \end{equation*}
In the above $\tau$ is the Frobenius-map, $P_{\infty}$ the point at infinity and as far as I'm understanding it right,$x$ beeing the $x$-coordinate from a Point $P'$. So it would be the $x$-coordinate from $(\overline{t}P')^q= \tau(\overline{t}P')= \overline{t}\tau(P')$
Can somebody tell me why the above is valid or does anybody have some hints?
I'd be very grateful.