The identification of essential variables of systems of algebraic equations applying Gauss- Jordan elimination

We propose, to the best of our knowledge, a new heuristic approach to the identification of a minimal essential set of variables of a system of algebraic equations, such as, for instance, a companion model of an electrical circuit. In particular we study the impact of numerical elimination (actually Gauss-Jordan elimination) for the case that the equation system contains a subset of linear constant equations with numerically known coefficients. The study reveals that the number of essential variables may be reduced substantially by elimination in some cases.