Dimensional Analysis in Mathematical Modeling Systems: A Simple Numerical Method

This paper discusses dimensional manipulation, essentially a problem requiring symbolic mathematics techniques, using a numerical approach. The numerical method obeys the laws of dimensional arithmetic. This is achieved by specifying an encoding of units of measurement as prime numbers, and manipulating the resulting expressions numerically. The unique factorization theorem is applied to show that this method makes trivial the problems of dimensional simplification and verification of dimensional equivalency, which are central issues in dimensional arithmetic. The solution has immediate application in mathematical modeling systems, chiefly in the model validation and model solution phases.