Pat, the definition of minimized system is not yet very clear. At the moment we assume that the definition is given by the code of minimize() because we have no clear ideas on what we really need. In general we can say that a system of constraints is minimized if it does not contain redundant constraints, but we want it also to be normalized (the GCD of the coefficient must be 1).
Since minimize() is too expensive, in the PPL we use the flag 'minimized' and we want that when it is set, the system is minimized in the sense that we can avoid to invoke minimize(). To check if this flag is handled, we use OK(): it takes a system, makes a copy and calls minimize, then compare it with the system having flag minimized set, after invoking gauss(), backsubstitute(), sorting and normalizing it. If the two system are equal, it means that the flag is correctly handled and when it is set the matrix is minimized.
I hope I'm not make you confused.
Ciao, Angela.