  We perform a study of matrix elements relevant for the Delta I=1/2 rule and
the direct CP-violation parameter epsilon-prime from first principles by
computer simulation in Lattice QCD. We use staggered (Kogut-Susskind) fermions,
and employ the chiral perturbation theory method for studying K to 2 Pi decays.
Having obtained a reasonable statistical accuracy, we observe an enhancement of
the Delta I=1/2 amplitude, consistent with experiment within our large
systematic errors. Finite volume and quenching effects have been studied and
were found small compared to noise. The estimates of epsilon-prime are hindered
by large uncertainties associated with operator matching. In this paper we
explain the simulation method, present the results and address the systematic
uncertainties.
