  We enumerate the local Petrovskii lacunas (that is, the domains of local
regularity of the principal fundamental solutions) of strictly hyperbolic PDE's
with constant coefficients in $R^N$ at the parabolic singular points of their
wavefronts. These points form the next difficult family of classes of the
natural classification of singular points after the so-called simple
singularities, studied previously.
  Also we promote a computer program counting for topologically different
morsifications of critical points of smooth functions, and hence also for local
components of the complement of a generic wavefront at its singular points.
