Normaliz is a free

computer algebra system A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The de ...

developed by Winfried Bruns, Robert Koch (1998–2002), Bogdam Ichim (2007/08) and Christof Soeger (2009–2016). It is published under the

GNU General Public License The GNU General Public Licenses (GNU GPL or simply GPL) are a series of widely used free software licenses, or ''copyleft'' licenses, that guarantee end users the freedom to run, study, share, or modify the software. The GPL was the first ...

version 2. Normaliz computes lattice points in rational

polyhedra In geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. The term "polyhedron" may refer either to a solid figure or to its boundary su ...

, or, in other terms, solves linear diophantine systems of equations, inequalities, and congruences. Special tasks are the computation of lattice points in bounded rational polytopes and Hilbert bases of rational cones. Normaliz also computes enumerative data, such as multiplicities (volumes) and

Hilbert series In commutative algebra, the Hilbert function, the Hilbert polynomial, and the Hilbert series of a graded commutative algebra finitely generated over a field are three strongly related notions which measure the growth of the dimension of the homog ...

. The kernel of Normaliz is a templated C++ class library. For multivariate polynomial arithmetic it uses CoCoALib. Normaliz has interfaces to several general computer algebra systems: CoCoA, GAP,

Macaulay2 Macaulay2 is a free computer algebra system created by Daniel Grayson (from the University of Illinois at Urbana–Champaign) and Michael Stillman (from Cornell University) for computation in commutative algebra and algebraic geometry. Overview ...

and

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. It can be used interactively via its Python interface PyNormaliz. Its use in SageMath is in preparation. Jesús A. De_Loera cites Normaliz among his favorite programs for computing Hilbert basis.

References

External links

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Publications and examples of Normaliz applications
*http://github.com/normaliz/Normaliz {{Computer algebra systems Computer algebra system software for Linux Computer algebra system software for macOS Computer algebra system software for Windows Cross-platform free software Free computer algebra systems Computer algebra systems

See also

References

External links