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# Convex

## A GAP package for handling convex objects.

Version 2015.11.06

August 2012

This manual is best viewed as an HTML document. An offline version should be included in the documentation subfolder of the package.

Sebastian Gutsche
Email: sebastian.gutsche@rwth-aachen.de
Homepage: http://wwwb.math.rwth-aachen.de/~gutsche
Address:
Lehrstuhl B für Mathematik, RWTH Aachen, Templergraben 64, 52056 Aachen, Germany

### Copyright

© 2011-2012 by Sebastian Gutsche

This package may be distributed under the terms and conditions of the GNU Public License Version 2.

### Acknowledgements

### Contents

1 Introduction
1.1 What is the goal of the Convex package?
2 Installation of the Convex Package
3 Convex Objects
3.1 Convex Objects: Category and Representations
3.1-1 IsConvexObject
3.2 Convex objects: Properties
3.2-1 IsFullDimensional
3.3 Convex objects: Attributes
3.3-1 Dimension
3.3-2 AmbientSpaceDimension
3.3-3 ContainingGrid
3.4 Convex objects: Methods
3.4-1 DrawObject
3.4-2 WeakPointerToExternalObject
4 Fan
4.1 Fan: Category and Representations
4.1-1 IsFan
4.2 Fan: Properties
4.2-1 IsComplete
4.2-2 IsPointed
4.2-3 IsSmooth
4.2-4 IsRegularFan
4.2-5 IsSimplicial
4.2-6 HasConvexSupport
4.3 Fan: Attributes
4.3-1 Rays
4.3-2 RayGenerators
4.3-3 RaysInMaximalCones
4.3-4 MaximalCones
4.4 Fan: Methods
4.4-1 *
4.5 Fan: Constructors
4.5-1 Fan
4.5-2 Fan
4.6 Fan: Examples
4.6-1 Fan example
5 Cone
5.1 Cone: Category and Representations
5.1-1 IsCone
5.2 Cone: Properties
5.2-1 IsRay
5.3 Cone: Attributes
5.3-1 DualCone
5.3-2 HilbertBasis
5.3-3 RaysInFacets
5.3-4 Facets
5.3-5 GridGeneratedByCone
5.3-6 FactorGrid
5.3-7 GridGeneratedByOrthogonalCone
5.3-8 DefiningInequalities
5.3-9 IsContainedInFan
5.3-10 FactorGridMorphism
5.4 Cone: Methods
5.4-1 IntersectionOfCones
5.4-2 Contains
5.4-3 StarFan
5.4-4 StarFan
5.4-5 StarSubdivisionOfIthMaximalCone
5.5 Cone: Constructors
5.5-1 Cone
5.6 Cone: Examples
5.6-1 Cone example
6 Polytope
6.1 Polytope: Category and Representations
6.1-1 IsPolytope
6.2 Polytope: Properties
6.2-1 IsNotEmpty
6.2-2 IsLatticePolytope
6.2-3 IsVeryAmple
6.2-4 IsNormalPolytope
6.2-5 IsSimplicial
6.2-6 IsSimplePolytope
6.3 Polytope: Attributes
6.3-1 Vertices
6.3-2 LatticePoints
6.3-3 FacetInequalities
6.3-4 VerticesInFacets
6.3-5 AffineCone
6.3-6 NormalFan
6.3-7 RelativeInteriorLatticePoints
6.4 Polytope: Methods
6.4-1 *
6.4-2 #
6.5 Polytope: Constructors
6.5-1 Polytope
6.5-2 PolytopeByInequalities
6.6 Polytope: Examples
6.6-1 Polytope example
Index
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