We discuss an equation analyser which analyses matrix structure to detect incorrect specification in equation systems and identifies free variables. Structural analysis uses output assignment to find a trial set of free variables. The choice is affected by the rules for output variable selection in each equation and to a lesser extent by how the equations are reordered.Numerical singularity is found by attempting Gaussian elimination of the initial Jacobian. Causes include dependent equations or an unsuitable starting guess. Element type codes distinguish constant and variable Jacobian elements. Rules for element type arithmetic are presented. The equation analyser cannot distinguish a singular guess from nonlinear dependence, which may be detected if singularity persists in a partial solution at later iterations. We show the free variable choices and ease of solution for the corresponding simulations are presented in three examples with between 22 and 60 variables. Rules for equation ordering and output variable assignment are proposed.