  Extending previous results we show that there are no Petrov type III
space-times on which either the Weyl neutrino equation or Maxwell's equations
satisfy Huygens' principle. We prove the result by using Maple's NPspinor
package to convert the five-index necessary condition obtained by Alvarez and
Wunsch to dyad form. The integrability conditions of the problem lead to a
system of polynomial equations. We then apply Maple's grobner package to show
that this system has no admissible solutions.
