Integer programming techniques can be used in the characterization of relations between the variables of programs. Such techniques are considered to be far too expensive to be used in an automatic optimizing tool. We show that the cost of such a technique can be balanced by the quality of the information that can be extracted. Our algorithm transforms sets of equations and constraints that are extracted, by the optimizing compiler from programs and produces a characterization of the solution domain of the system. The result is a restricted domain of possible values for each variable as well as a set of new pertinent constraints. The system is run incrementally from the compiler. Its application domain is not limited to the computation of dependencies. In fact, it can be useful everywhere the decision of the compiler depends on the characterization of relations between variables of the program.