  Let $q$ be a prime power and let $G$ be an absolutely irreducible subgroup of
$GL_d(F)$, where $F$ is a finite field of the same characteristic as $\F_q$,
the field of $q$ elements. Assume that $G \cong G(q)$, a quasisimple group of
exceptional Lie type over $\F_q$ which is neither a Suzuki nor a Ree group. We
present a Las Vegas algorithm that constructs an isomorphism from $G$ to the
standard copy of $G(q)$. If $G \not\cong {}^3 D_4(q)$ with $q$ even, then the
algorithm runs in polynomial time, subject to the existence of a discrete log
oracle.
