Normaliz: A package for linear diophantine systems, polyhedra and lattices

Abstract

The very first version of Normaliz [5] was meant to compute normalizations of affine monoids (or semi- groups), hence the name. Over the years it has been extended to a powerful package for discrete convex geometry. We explain its main computation goals by a simple example, sketch the mathematical background and discuss the basic steps in the Normaliz primal algorithm. Some remarks on the technical aspects and the history conclude this overview.