# Minimal polynomial in tower of finite fields?

I have two extension field $E=K(d)$ and $K=F(a)$ where $F=GF(p)$ for a prime $p$. How can I compute the minimal polynomial of $d$ over $F$. There is a command "absolute_minpoly" that works for number fields and not extension fields of finite fields. I want a command like that.

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I suppose we know the minimal polynomial of $d$ over $F=\Bbb F_p$. We can factor it over $K$....