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NConvex

A Gap package to perform polyhedral computations

2022.09-01

30 September 2022

Kamal Saleh
Email: kamal.saleh@uni-siegen.de
Homepage: https://github.com/kamalsaleh
Address:
Department Mathematik
Universität Siegen
Walter-Flex-Straße 3
57068 Siegen
Germany

Sebastian Gutsche
Email: gutsche@mathematik.uni-siegen.de
Homepage: https://sebasguts.github.io/
Address:
Department Mathematik
Universität Siegen
Walter-Flex-Straße 3
57068 Siegen
Germany

Contents

1 Introduction
 1.1 Installation
 1.2 Requirements
2 Functionality
3 Convex objects
 3.1 Attributes

  3.1-1 AmbientSpaceDimension
  3.1-2 Dimension
  3.1-3 IsFullDimensional
  3.1-4 InteriorPoint
4 Cones
 4.1 Creating cones

  4.1-1 ConeByInequalities
  4.1-2 ConeByEqualitiesAndInequalities
  4.1-3 Cone
  4.1-4 Cone
 4.2 Attributes of Cones

  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 Properties of Cones

  4.3-1 IsRegularCone
  4.3-2 IsRay
  4.3-3 IsZero
 4.4 Operations on cones

  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 Fans
 5.1 Constructors

  5.1-1 Fan
  5.1-2 Fan
  5.1-3 Fan
  5.1-4 FansFromTriangulation
  5.1-5 FanFromTriangulation
 5.2 Attributes

  5.2-1 RayGenerators
  5.2-2 GivenRayGenerators
  5.2-3 RaysInMaximalCones
  5.2-4 MaximalCones
  5.2-5 FVector
 5.3 Properties

  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 Operations on fans
6 Polyhedrons
 6.1 Creating polyhedron

  6.1-1 PolyhedronByInequalities
  6.1-2 Polyhedron
  6.1-3 Polyhedron
  6.1-4 Polyhedron
  6.1-5 Polyhedron
 6.2 Attributes

  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 Properties

  6.3-1 IsBounded
  6.3-2 IsPointed
 6.4 Solving Linear programs

  6.4-1 SolveLinearProgram
  6.4-2 SolveLinearProgram
 6.5 ZSolve

  6.5-1 SolveEqualitiesAndInequalitiesOverIntergers
7 Polytopes
 7.1 Creating polytopes

  7.1-1 PolytopeByInequalities
  7.1-2 Polytope
 7.2 Attributes

  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 Properties

  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 Operations on polytopes

  7.4-1 \+
  7.4-2 \*
  7.4-3 IntersectionOfPolytopes
  7.4-4 RandomInteriorPoint
  7.4-5 IsInteriorPoint
Index

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