The Polyhedral Model has been an academic topic since the early eighties. It has primarily been used for systolic architecture generation and loop tranformations. During the last ten years, interest in this model has increased for many reasons: computing power has increased (Polyhedral Model is compute intensive), classical heuristic loop transformation methods have reached their limits, architectural behaviour is becoming unpredictable because of its complexity and new hardware (like graphic accelerators) are opening new horizons. This report presents the implementation in ROSE, a research compiler, of Farkas' Algorithm. A new way to apply this algorithm has been developed; this variation of the original algorithm enables elimination of all hidden variables created by Farkas' Algorithm. This algorithm can also be applied in parallel to use multicore processors, alleviating the cost of the modification.