Coefficients of an orbit polynomial for a primitive generator
= Coefficients of an orbit polynomial for a primitive generator
If $K\subseteq L^G$ and $L=K(\alpha)$, then the coefficients of $f(t,\alpha)$ generate $L^G$ over $K$. Indeed, for the field $E$ generated by those coefficients, $L=E(\alpha)$ and $[L:E]\leq|G|$, while the <Artin fixed-field theorem> gives $[L:L^G]=|G|$.