A SIMPLE CRITERION FOR INVOLUTIVITY

A simple criterion for the involutivity of a system of partial differe ntial equations of polynomial type is proved. The criterion involves t he equations themselves and does not require the system to be in ortho nomic form. It is proved that a system of partial differential equatio ns is involutive if it is a differential Grobner basis with respect to a total degree ordering, and if the compatibility conditions of the s ymbol equations of the system consist of equations of degree one. An a lgorithm for calculating these compatibility conditions is given.