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Normaliz

From Wikipedia, the free encyclopedia
Computer algebra system
Normaliz
Original authorsWinfried Bruns, Robert Koch, Bogdan Ichim, Christof Soeger
Stable release
3.11.0[1] / 18 October 2025; 4 months ago (18 October 2025)
Written inC++,C andPython
TypeComputer algebra system
LicenseGNU General Public License, version 3
Websitenormaliz.uni-osnabrueck.de
Repository

Normaliz is afreecomputer algebra system developed by Winfried Bruns, Robert Koch (1998–2002), Bogdam Ichim (2007/08) and Christof Soeger (2009–2016). It is published under theGNU General Public License version 2.

Normaliz computes lattice points in rationalpolyhedra, or, in other terms, solveslinear diophantine systems of equations, inequalities, and congruences. Special tasks are the computation of lattice points in bounded rational polytopes andHilbert bases of rational cones. Normaliz also computes enumerative data, such as multiplicities (volumes) andHilbert series. The kernel of Normaliz is a templated C++ class library. For multivariate polynomial arithmetic it usesCoCoALib.

Normaliz has interfaces to several general computer algebra systems:CoCoA,GAP,Macaulay2 andSingular. 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 computingHilbert basis.[2]

See also

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References

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  1. ^"Release 3.11.0". 18 October 2025. Retrieved20 October 2025.
  2. ^De Loera, Jesús. "Combinatorial Problems with Geometric Solutions".Course Notes: Algebraic and Geometric Combinatorics. UC Davis.

External links

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Open-source
Proprietary
Discontinued
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