Winfried Bruns, Tim Römer, Richard Sieg and Christof Söger




The Normaliz project is supported by the DFG SPP 1489

"Algorithmische und experimentelle Methoden in Algebra, Geometrie und Zahlentheorie"




Normaliz is a tool for computations in affine monoids, vector configurations, lattice polytopes, and rational cones.


Its input data can be specified in terms of



Normaliz computes



Normaliz can be started from the command line or from the GUI interface jNormaliz (written by Vinicius Almendra and Bogdan Ichim). jNormaliz is included in the distribution. See the Normaliz documentation for details.


The user indicates the type of input data in the input file and controls the computation and the output via the GUI interface or command line options.


Normaliz is provided for 2 degrees of integer precision: 64 bits or infinite. For infinite precision it uses the GMP (Linux, Mac) and MPIR (Windows) libraries. Normaliz checks for overflows and switches to infinite precision if necessary.


NmzIntegrate is based on CoCoALib.


Normaliz comes with interfaces for Macaulay2 and Singular. The Macaulay2 interface (written by Gesa Kämpf) needs Macaulay2 1.1.99 or later. The Singular interface needs Singular 3-0-0 or later. Normaliz is accessible from polymake (thanks to an interface written by the polymake team) and is used by B. Burton's Regina. Normaliz has interfaces to CoCoA and GAP.


Some interesting and challenging examples document the power of Normaliz.  Please send examples that you would like to add to the collection to one of the authors!


References to articles about Normaliz are included in the documentation and their pdf files can be found in the distribution.


Normaliz is distributed under GPL.


Please subscribe to our mailing list by sending an empty email to . We will keep you up-to-date in regard to new versions and bugfixes.


Current version: 3.0.0 (including NmzIntegrate 1.3) (uploaded September 28, 2015) Previous versions: 2.12.2  2.11.2  2.10.1  2.8   2.7   2.5


Download and installation


Normaliz history