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Consider any algebraic number $\alpha$ which is given by its minimal polynomial $f$. How can I compute the minimal polynomial of $\alpha^m$ for some natural number $m$? How efficient the algorithm is?

I assume that this problem is well-studied, but can anyone give me a reference, or some short description of the algorithm?

Thanks a lot!

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    I think the minimal polynomial of $\alpha$ and the minimal polynomial of $\alpha^m$ are not strongly related. (Except of course in some special cases.)2012-10-19
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    thanks. Somehow this question can be formulated as given $\alpha$, how to compute (symbolically) $\alpha^m$. I guess there must be some algorithm to do so.2012-10-19

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