Practical issues on the projection of polyhedral sets

Projection of polyhedral sets is a fundamental operation in both geometry and symbolic computation. In most cases, however, it is not practically feasible to generate projections as the size of the output can be exponential in the size of the input. Even when the size of the output is manageable, we still face two serious problems: overwhelming redundancy and degeneracy. Here, we address these problems from a practical point of view. We discuss three algorithms based on algebraic and geometric techniques and we compare their performance in order to assess the feasibility of these approaches.