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# NormalizInterface

## GAP wrapper for Normaliz

0.9.8

07/05/2016

Sebastian Gutsche
Email: gutsche@mathematik.uni-kl.de
Homepage: http://wwwb.math.rwth-aachen.de/~gutsche/
Address:
Department of Mathematics
University of Kaiserslautern
67653 Kaiserslautern
Germany

Max Horn
Email: max.horn@math.uni-giessen.de
Homepage: http://www.quendi.de/math
Address:
AG Algebra
Mathematisches Institut
Justus-Liebig-Universität Gießen
Arndtstraße 2
35392 Gießen
Germany

Christof Söger
Email: csoeger@uos.de
Homepage: https://www.normaliz.uni-osnabrueck.de
Address:
Institut für Mathematik
Albrechtstr. 28a
49076 Osnabrück
Germany

### Contents

1 Introduction
1.1 What is the purpose of the this package?
2 Functions
2.1 Create a NmzCone
2.1-1 NmzCone
2.2 Use a NmzCone
2.2-1 NmzHasConeProperty
2.2-2 NmzKnownConeProperties
2.2-3 NmzSetVerboseDefault
2.2-4 NmzSetVerbose
2.2-5 NmzCompute
2.2-6 NmzConeProperty
2.2-7 NmzPrintConeProperties
2.3 Cone properties
2.3-1 NmzEmbeddingDimension
2.3-2 NmzRank
2.3-3 NmzIsInhomogeneous
2.3-4 NmzEquations
2.3-5 NmzCongruences
2.3-6 NmzAffineDim
2.3-7 NmzClassGroup
2.3-8 NmzDeg1Elements
2.3-9 NmzDehomogenization
2.3-10 NmzExcludedFaces
2.3-11 NmzExtremeRays
2.3-12 NmzGenerators
2.3-13 NmzGrading
2.3-14 NmzHilbertBasis
2.3-15 NmzHilbertQuasiPolynomial
2.3-16 NmzHilbertSeries
2.3-17 NmzInclusionExclusionData
2.3-18 NmzIsDeg1ExtremeRays
2.3-19 NmzIsDeg1HilbertBasis
2.3-20 NmzIsIntegrallyClosed
2.3-21 NmzIsPointed
2.3-22 NmzMaximalSubspace
2.3-23 NmzModuleGenerators
2.3-24 NmzModuleGeneratorsOverOriginalMonoid
2.3-25 NmzModuleRank
2.3-26 NmzMultiplicity
2.3-27 NmzOriginalMonoidGenerators
2.3-28 NmzRecessionRank
2.3-29 NmzIsReesPrimary
2.3-30 NmzReesPrimaryMultiplicity
2.3-31 NmzSupportHyperplanes
2.3-32 NmzTriangulation
2.3-33 NmzTriangulationDetSum
2.3-34 NmzTriangulationSize
2.3-35 NmzVerticesOfPolyhedron
2.3-36 NmzBasisChange
3 Examples
3.1 Generators
3.2 System of equations
3.3 System of inhomogeneous equations
3.4 Combined input
3.5 Using the dual mode
4 Installing NormalizInterface
4.1 Compiling
References
Index
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