  Let E be a torsion-free sheaf on P2. We give an effective method which uses
the Hilbert function of E to construct a weak version of the Harder-Narasimhan
filtration of a torsion-free sheaf on P2 subject only to the condition that E
be sufficiently general among sheaves with that Hilbert function. This
algorithm uses on a generalization of Davis' decomposition lemma to higher
rank.
