chap0.txt

  
  
                                     Convex
  
  
                   A GAP package for handling convex objects.
  
  
                               Version 2013.12.05
  
  
                                  August 2012
  
  
                               Sebastian Gutsche
  
  
  
            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:    mailto:[email protected]
      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 (Convex)
  
  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