W. Bruns: Normaliz: algorithms for rational cones and affine monoids.

Abstract. Normaliz is a computer program for the computation of Hilbert bases of rational cones and related tasks. Its main application in commutative algebra is the (equivalent) computation of integral closures of an affine monoid (or its algebra) in a surrounding lattice (or the corresponding group algebra). The first version was developed by the speaker and R. Koch in 1997-2001, and the new version 2 was recently implemented by B. Ichim. It has improved the first version in several aspects.

There are Normaliz packages for Singular and Macaulay 2 (the latter written by G. Kämpf). We will explain the algorithms and demonstrate the program and the packages.