A method is presented that reduces the number of terms of systems of linear
equations (algebraic, ordinary and partial differential equations). As a
byproduct these systems have a tendency to become partially decoupled and are
more likely to be factorizable or integrable. A variation of this method is
applicable to non-linear systems. Modifications to improve efficiency are given
and examples are shown. This procedure can be used in connection with the
computation of the radical of a differential ideal (differential Groebner
basis)