A new method for variable elimination in systems of inequations

In this paper, we present a new method for variable elimination in systems of inequalities which is much faster than the Fourier-Motzkin Elimination (FME) method. In our method, a linear Diophantine problem is introduced which is dual to the original problem. The new Diophantine system is then solved, and the final result is calculated by finding the dual system of inequalities. This new method uses the algorithm Normaliz to find the Hilbert basis of the solution space of the given Diophantine problem. We introduce a problem in the interference channel with multiple nodes and solve it with this new method. Next, we generalize our method to all problems involving FME and compare the method with the previous method. Our method has many advantages in comparison to the previous method. It does not produce many of the redundant answers of the FME method. It also solves the whole problem in one step whereas the previous method uses a step by step approach in eliminating each auxiliary variable.