It was known that the various higher partial derivatives of a set of c general enough polynomialsof specified degrees are as independent as possible. We generalize this result to a set of c general enough elements of the direct sum Ps. The power series ringacts as partial differential operators on Ps; the Matlis duality relates A-submodulesof Psand quotients [Mbar] of As. The degrees ofdetermine the socle type of [Mbar] . A quotient [Mbar] of Asis termed compressed if it has maximal length given {r,s, socle type of [Mbar]}. A compressed module [Mbar] is the Matlis dual to a set of elementsof specified degrees in Ps, whose partial derivatives of all orders are as independent as possible.