  Mathematica offers, by way of the package Combinatorics, many useful
functions to work on graphs and ordered structures, but none of these functions
was specific enough to meet the needs of our research group. Moreover, the
existing functions are not always helpful when one has to work on new concepts.
  In this paper we present a package of features developed in Mathematica which
we consider particularly useful for the study of certain categories of
partially ordered sets. Among the features offered, the package includes: (1)
some basic features to treat partially ordered sets; (2) the ability to
enumerate, create, and display monotone and regular partitions of partially
ordered sets; (3) the capability of constructing the lattices of partitions of
a poset, and of doing some useful computations on these structures; (4) the
possibility of computing products and coproducts in the category of partially
ordered sets and monotone maps; (5) the possibility of computing products and
coproducts in the category of forests (disjoint union of trees) and open maps
(cf. [DM06] for the product between forests).
