  We develop a method to compute the Ekedahl-Oort type of a curve C over a
field k of characteristic p (which is the isomorphism type of the p-kernel
group scheme J[p], where J is the Jacobian of C). Part of our method is
general, in that we introduce the new notion of a Hasse-Witt triple, which
re-encodes in a useful way the information contained in the Dieudonne module of
J[p]. For complete intersection curves we then give a simple method to compute
this Hasse-Witt triple. An implementation of this method is available in Magma.
