  
  
                                   [1X NConvex [101X
  
  
               [1X A Gap package to perform polyhedral computations [101X
  
  
                                   2022.09-01
  
  
                               30 September 2022
  
  
                                  Kamal Saleh
  
                               Sebastian Gutsche
  
  
  
  Kamal Saleh
      Email:    [7Xmailto:kamal.saleh@uni-siegen.de[107X
      Homepage: [7Xhttps://github.com/kamalsaleh[107X
      Address:  [33X[0;14YDepartment Mathematik[133X
                [33X[0;14YUniversität Siegen[133X
                [33X[0;14YWalter-Flex-Straße 3[133X
                [33X[0;14Y57068 Siegen[133X
                [33X[0;14YGermany[133X
  
  
  Sebastian Gutsche
      Email:    [7Xmailto:gutsche@mathematik.uni-siegen.de[107X
      Homepage: [7Xhttps://sebasguts.github.io/[107X
      Address:  [33X[0;14YDepartment Mathematik[133X
                [33X[0;14YUniversität Siegen[133X
                [33X[0;14YWalter-Flex-Straße 3[133X
                [33X[0;14Y57068 Siegen[133X
                [33X[0;14YGermany[133X
  
  
  
  -------------------------------------------------------
  
  
  [1XContents (NConvex)[101X
  
  1 [33X[0;0YIntroduction[133X
    1.1 [33X[0;0YInstallation[133X
    1.2 [33X[0;0YRequirements[133X
  2 [33X[0;0YFunctionality[133X
  3 [33X[0;0YConvex objects[133X
    3.1 [33X[0;0YAttributes[133X
      3.1-1 AmbientSpaceDimension
      3.1-2 Dimension
      3.1-3 IsFullDimensional
      3.1-4 InteriorPoint
  4 [33X[0;0YCones[133X
    4.1 [33X[0;0YCreating cones[133X
      4.1-1 ConeByInequalities
      4.1-2 ConeByEqualitiesAndInequalities
      4.1-3 Cone
      4.1-4 Cone
    4.2 [33X[0;0YAttributes of Cones[133X
      4.2-1 DefiningInequalities
      4.2-2 EqualitiesOfCone
      4.2-3 DualCone
      4.2-4 FacesOfCone
      4.2-5 Facets
      4.2-6 FVector
      4.2-7 RelativeInteriorRay
      4.2-8 HilbertBasis
      4.2-9 HilbertBasisOfDualCone
      4.2-10 LinealitySpaceGenerators
      4.2-11 ExternalCddCone
      4.2-12 ExternalNmzCone
      4.2-13 AmbientSpaceDimension
      4.2-14 LatticePointsGenerators
      4.2-15 GridGeneratedByCone
      4.2-16 FactorGrid
      4.2-17 FactorGridMorphism
      4.2-18 GridGeneratedByOrthogonalCone
    4.3 [33X[0;0YProperties of Cones[133X
      4.3-1 IsRegularCone
      4.3-2 IsRay
      4.3-3 IsZero
    4.4 [33X[0;0YOperations on cones[133X
      4.4-1 FourierProjection
      4.4-2 IntersectionOfCones
      4.4-3 IntersectionOfCones
      4.4-4 Contains
      4.4-5 IsRelativeInteriorRay
      4.4-6 NonReducedInequalities
  5 [33X[0;0YFans[133X
    5.1 [33X[0;0YConstructors[133X
      5.1-1 Fan
      5.1-2 Fan
      5.1-3 Fan
      5.1-4 FansFromTriangulation
      5.1-5 FanFromTriangulation
    5.2 [33X[0;0YAttributes[133X
      5.2-1 RayGenerators
      5.2-2 GivenRayGenerators
      5.2-3 RaysInMaximalCones
      5.2-4 MaximalCones
      5.2-5 FVector
    5.3 [33X[0;0YProperties[133X
      5.3-1 IsWellDefinedFan
      5.3-2 IsComplete
      5.3-3 IsPointed
      5.3-4 IsSmooth
      5.3-5 IsSimplicial
      5.3-6 IsNormalFan
      5.3-7 IsRegularFan
      5.3-8 IsFanoFan
    5.4 [33X[0;0YOperations on fans[133X
  6 [33X[0;0YPolyhedrons[133X
    6.1 [33X[0;0YCreating polyhedron[133X
      6.1-1 PolyhedronByInequalities
      6.1-2 Polyhedron
      6.1-3 Polyhedron
      6.1-4 Polyhedron
      6.1-5 Polyhedron
    6.2 [33X[0;0YAttributes[133X
      6.2-1 ExternalCddPolyhedron
      6.2-2 ExternalNmzPolyhedron
      6.2-3 DefiningInequalities
      6.2-4 MainRatPolytope
      6.2-5 MainPolytope
      6.2-6 VerticesOfMainRatPolytope
      6.2-7 VerticesOfMainPolytope
      6.2-8 TailCone
      6.2-9 RayGeneratorsOfTailCone
      6.2-10 LatticePointsGenerators
      6.2-11 BasisOfLinealitySpace
      6.2-12 FVector
    6.3 [33X[0;0YProperties[133X
      6.3-1 IsBounded
      6.3-2 IsPointed
    6.4 [33X[0;0YSolving Linear programs[133X
      6.4-1 SolveLinearProgram
      6.4-2 SolveLinearProgram
    6.5 [33X[0;0YZSolve[133X
      6.5-1 SolveEqualitiesAndInequalitiesOverIntergers
  7 [33X[0;0YPolytopes[133X
    7.1 [33X[0;0YCreating polytopes[133X
      7.1-1 PolytopeByInequalities
      7.1-2 Polytope
    7.2 [33X[0;0YAttributes[133X
      7.2-1 ExternalCddPolytope
      7.2-2 LatticePoints
      7.2-3 RelativeInteriorLatticePoints
      7.2-4 VerticesOfPolytope
      7.2-5 Vertices
      7.2-6 DefiningInequalities
      7.2-7 EqualitiesOfPolytope
      7.2-8 FacetInequalities
      7.2-9 VerticesInFacets
      7.2-10 NormalFan
      7.2-11 FaceFan
      7.2-12 AffineCone
      7.2-13 PolarPolytope
      7.2-14 DualPolytope
    7.3 [33X[0;0YProperties[133X
      7.3-1 IsEmpty
      7.3-2 IsLatticePolytope
      7.3-3 IsVeryAmple
      7.3-4 IsNormalPolytope
      7.3-5 IsSimplicial
      7.3-6 IsSimplexPolytope
      7.3-7 IsSimplePolytope
      7.3-8 IsReflexive
      7.3-9 IsFanoPolytope
      7.3-10 IsCanonicalFanoPolytope
      7.3-11 IsTerminalFanoPolytope
      7.3-12 IsSmoothFanoPolytope
    7.4 [33X[0;0YOperations on polytopes[133X
      7.4-1 \+
      7.4-2 \*
      7.4-3 IntersectionOfPolytopes
      7.4-4 RandomInteriorPoint
      7.4-5 IsInteriorPoint
  
  
  [32X
