  This paper represents a detailed instruction manual for constructing the
Landau expansion for magnetoelectric coupling in incommensurate ferroelectric
magnets. The first step is to describe the magnetic ordering in terms of
symmetry adapted coordinates which serve as complex valued magnetic order
parameters whose transformation properties are displayed. In so doing we use
the previously proposed technique to exploit inversion symmetry, since this
symmetry had been universally overlooked. Having order parameters of known
symmetry which describe the magnetic ordering, we are able to construct the
trilinear interaction which couples incommensurate magnetic order to the
uniform polarization in order to treat many of the multiferroic systems so far
investigated. The role of this theory in comparison to microscopic models is
discussed.
