  We present a computational tool that can be used to obtain the "spatial"
homology groups of a causal set. Localisation in the causal set is seeded by an
inextendible antichain, which is the analog of a spacelike hypersurface, and a
one parameter family of nerve simplicial complexes is constructed by
"thickening" this antichain. The associated homology groups can then be
calculated using existing homology software, and their behaviour studied as a
function of the thickening parameter. Earlier analytical work showed that for
an inextendible antichain in a causal set which can be approximated by a
globally hyperbolic spacetime region, there is a one parameter sub-family of
these simplicial complexes which are homological to the continuum, provided the
antichain satisfies certain conditions. Using causal sets that are approximated
by a set of 2d spacetimes our numerical analysis suggests that these conditions
are generically satisfied by inextendible antichains. In both 2d and 3d
simulations, as the thickening parameter is increased, the continuum homology
groups tend to appear as the first region in which the homology is constant, or
"stable" above the discreteness scale. Below this scale, the homology groups
fluctuate rapidly as a function of the thickening parameter. This provides a
necessary though not sufficient criterion to test for manifoldlikeness of a
causal set.
