  In any type II superstring background, the supergravity vertex operators in
the pure spinor formalism are described by a gauge superfield. In this paper,
we obtain for the first time an explicit expression for this superfield in an
$AdS_5 \times S^5$ background. Previously, the vertex operators were only known
close to the boundary of $AdS_5$ or in the minus eight picture. Our strategy
for the computation was to apply eight picture raising operators in the minus
eight picture vertices. In the process, a huge number of terms are generated
and we have developed numerical techniques to perform intermediary
simplifications. Alternatively, the same numerical techniques can be used to
compute the vertices directly in the zero picture by constructing a basis of
invariants and fitting for the coefficients. One motivation for constructing
the vertex operators is the computation of $AdS_5 \times S^5$ string
amplitudes.
