As pre-processing we distinguish the elimination of points in advance that do not contribute to the mixed volume and the combination with product structures.
For the first task we have not only included the possibility of omitting the nonvertex points but also a more sophisticated criterion has been developed. To combine product and polyhedral homotopies, for some equations we decompose the polytopes as the sum of smaller ones. This yields a significant speed up of the solver. The current implementation only allows to submit a set structure for some of the equations and contains no other support for guiding the choice of the decomposition.
For the lifting methods based on mixed subdivisions, the last stage is the computation of the mixed volume. A subdivision may not be fine enough so that simple determinant computations suffice. The program then applies a lifting method again, but only on those cells that are not fine. The subdivisions of the cells that arise in this way are stored themselves in a recursive data structure, which is useful for polyhedral continuation.