The GHP II package with applications

We present an advanced version of the Maple package GHP called GHPII. In it we provide a number of additional sophisticated tools to assist with problems formulated in the Geroch-Held-Penrose (ghp) formalism. The first part of this article discusses these new tools while in the second part we shall apply the ghp formalism, using the GHPII routines, to vacuum Petrov type D spacetimes and shear-free perfect fluids. We prove that for all shear-free perfect fluids with a barotropic equation of state, where two of the principal null directions are coplanar with the fluid four-velocity and vorticity then either the expansion or vorticity of the fluid must be zero.