The tool RoCo allows to compute various root counts for one system. Corresponding to each root count, a start system can be constructed, which leads to a homotopy with exactly as many paths as the underlying root count.
After the default computation of the total degree, RoCo offers a menu of several root counting methods. The user can try various root counts before proceeding to the continuation stage. Deciding a priori which root count to choose is in general a hard problem which requires at least some partial information that is generated during root counting.
In this section we only describe the Bézout bounds. The decision to have a separate tool for mixed-volume computation is not only motivated by its importance but also because solving a random coefficient system is a task of higher complexity than solving a random linear-product system.