Normaliz is a free computer algebra system developed by Winfried Bruns, Robert Koch (1998–2002), Bogdam Ichim (2007/08) and Christof Soeger (2009–2016).

Normaliz computes lattice points in rational polyhedra, or, in other terms, solves linear diophantine systems of equations, inequalities, and congruences.

Normaliz also computes enumerative data, such as multiplicities (volumes) and Hilbert series.

Normaliz has interfaces to several general computer algebra systems: CoCoA, GAP, Macaulay2 and Singular.

Jesús A. De_Loera cites Normaliz among his favorite programs for computing Hilbert basis.