Mixed Volume Computation for Semi-Mixed Systems

Abstract. The Li—Li algorithm produced in [11] for the mixed volume computation of fully mixed polynomial systems is reconstructed in this article for general semi-mixed polynomial systems. Taking the special structure of the semi-mixed supports of the systems into account, the resulting algorithm, illustrated by numerical results, can dramatically speed up the mixed volume computation, especially when the systems are unmixed. Even when applied to fully mixed systems, the new algorithm improves the speed of the Li—Li algorithm by a considerable amount.