  Classical dimensional analysis is one of the cornerstones of qualitative
physics and is also used in the analysis of engineering systems, for example in
engineering design. The basic power product relationship in dimensional
analysis is identical to one way of defining toric ideals in algebraic
geometry, a large and growing field. This paper exploits the toric
representation to provide a method for automatic dimensional analysis for
engineering systems. In particular all "primitive", invariants for a particular
problem, in a well defined sense, can be found using such methods.
