  This is an expository version of our paper [arXiv:1902.07384]. Our aim is to
present recent Macaulay2 algorithms for computation of mixed multiplicities of
ideals in a Noetherian ring which is either local or a standard graded algebra
over a field. These algorithms are based on computation of the equations of
multi-Rees algebras of ideals that generalises a result of Cox, Lin and Sosa.
Using these equations we propose efficient algorithms for computation of mixed
volumes of convex lattice polytopes and sectional Milnor numbers of
hypersurfaces with an isolated singularity.
