Dimensional analysis using toric ideals

Abstract

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.