Solution
= Solution
Over the <finite field> $\mathbb F_{13}$,
$$
x^3-x^2+x+1=(x+2)(x^2-3x-6).
$$
The <discriminant> of the quadratic is $9+24\equiv7\pmod{13}$. The nonzero squares are $1,3,4,9,10,12$, so the quadratic is irreducible. Its two roots lie in $\mathbb F_{13^2}$, with the <Frobenius automorphism> interchanging them. Hence
$$
\boxed{\operatorname{Gal}(f)\cong C_2.}
$$