• OldPolyhedra -- for computations with convex polyhedra, cones, and fans
• affineHull -- computes the affine hull of a polyhedron
• affineImage -- computes the affine image of a cone or polyhedron
• affineImage(Matrix,Cone,Matrix) -- computes the affine image of a cone
• affineImage(Matrix,Polyhedron,Matrix) -- computes the affine image of a polyhedron
• affinePreimage -- computes the affine preimage of a cone or polyhedron
• affinePreimage(Matrix,Cone,Matrix) -- computes the affine preimage of a cone
• affinePreimage(Matrix,Polyhedron,Matrix) -- computes the affine preimage of a polyhedron
• ambDim -- ambient dimension of a Polyhedron, Cone or Fan
• areCompatible -- checks if the intersection of two cones/polyhedra is a face of each
• bipyramid -- computes the bipyramid over a polyhedron
• boundaryMap (missing documentation)
• ccRefinement -- computes the coarsest common refinement of a set of rays
• cellDecompose -- computes the regular cell decomposition
• commonFace -- checks if the intersection is a face of both Cones or Polyhedra, or of cones with fans
• Cone -- the class of all rational convex polyhedral cones
• Cone * Cone -- computes the direct product of two cones
• Cone * Polyhedron -- computes the direct product of a cone and a polyhedron
• Cone + Cone -- computes the Minkowski sum of two cones
• Cone + Polyhedron -- computes the Minkowski sum of a cone and a polyhedron
• Cone == Cone -- equality
• Cone ? Cone -- compares the Cones
• cones -- computes all cones of a fan of a certain dimension
• coneToPolyhedron -- converts a cone to class Polyhedron
• contains -- checks if the first argument contains the second argument
• convexHull -- computing the convex hull of points, rays and polyhedra
• crossPolytope -- computes the d-dimensional crosspolytope with diameter 2s
• cyclicPolytope -- computes the d dimensional cyclic polytope with n vertices
• dim(Cone) -- computes the dimension of a cone
• dim(Fan) -- computes the dimension of a fan
• dim(PolyhedralComplex) -- computes the dimension of a polyhedral complex
• dim(Polyhedron) -- computes the dimension of a polyhedron
• directProduct -- computes the direct product of two convex objects
• directProduct(Cone,Cone) -- computes the direct product of polyhedra and cones
• directProduct(Fan,Fan) -- computes the direct product of two fans
• dualCayley (missing documentation)
• dualCayleyFace (missing documentation)
• dualCone -- computes the dual Cone
• dualFaceLattice -- computes the dual face lattice of a cone or polyhedron
• dualFaceLattice(ZZ,Cone) -- computes the dual face lattice of a cone
• dualFaceLattice(ZZ,Polyhedron) -- computes the dual face lattice of a polyhedron
• ehrhart -- calculates the Ehrhart polynomial of a polytope
• emptyPolyhedron -- generates the empty polyhedron in n-space
• faceFan -- computes the fan generated by the cones over the faces
• faceLattice -- computes the face lattice of a cone or polyhedron
• faceLattice(ZZ,Cone) -- computes the face lattice of a cone
• faceLattice(ZZ,Polyhedron) -- computes the face lattice of a polyhedron
• faceOf (missing documentation)
• faces -- computes all faces of a certain codimension of a Cone or Polyhedron
• Fan -- the class of all fans
• fan -- generates a Fan
• Fan * Fan -- computes the direct product
• Fan == Fan -- equality
• fVector -- computes the f-vector of a Cone or Polyhedron
• halfspaces -- computes the defining half-spaces of a Cone or a Polyhedron
• hilbertBasis -- computes the Hilbert basis of a Cone
• hirzebruch -- computes the fan of the r-th Hirzebruch surface
• hypercube -- computes the d-dimensional hypercube with edge length 2*s
• hyperplanes -- computes the defining hyperplanes of a Cone or a Polyhedron
• imageFan -- computes the fan of the image
• incompCones -- returns the pairs of incompatible cones
• incompPolyhedra -- returns the pairs of incompatible polyhedra
• inInterior -- checks if a point lies in the relative interior of a Cone/Polyhedron
• interiorLatticePoints -- computes the lattice points in the relative interior of a polytope
• interiorPoint -- computes a point in the relative interior of the Polyhedron
• interiorVector -- computes a vector in the relative interior of a Cone
• intersection -- computes the intersection of half-spaces, hyperplanes, cones, and polyhedra
• isCompact -- checks compactness of a Polyhedron
• isComplete -- checks completeness of a Fan or PolyhedralComplex
• isEmpty -- checks if a Polyhedron is empty
• isFace -- tests if the first argument is a face of the second
• isLatticePolytope -- checks if a polyhedron is a lattice polytope
• isNormal(Polyhedron) -- checks if a polytope is normal in the ambient lattice
• isPointed -- checks if a Cone or Fan is pointed
• isPolytopal -- checks if a Fan is polytopal
• isPure -- checks if a Fan or PolyhedralComplex is of pure dimension
• isReflexive -- checks if a Polytope is reflexive
• isSimplicial -- checks if a polyhedral object is simplicial
• isSmooth -- checks if a Cone or Fan is smooth
• isVeryAmple -- checks if the Polyhedron is very ample
• latticePoints -- computes the lattice points of a polytope
• linSpace -- computes a basis of the lineality space
• maxCones -- displays the generating Cones of a Fan
• maxFace -- computes the face of a Polyhedron or Cone where a weight attains its maximum
• maxPolyhedra -- displays the generating Polyhedra of a PolyhedralComplex
• minFace -- computes the face of a Polyhedron or Cone where a weight attains its minimum
• minkowskiSum -- computes the Minkowski sum of two convex objects
• minkSummandCone -- computes the Cone of all Minkowski summands and the minimal decompositions
• mixedVolume -- computes the mixed volume of a list of polytope
• net(Cone) -- displays characteristics of a cone
• net(Fan) -- displays characteristics of a fan
• net(PolyhedralComplex) -- displays characteristics of a polyhedral complex
• net(Polyhedron) -- displays characteristics of a polyhedron
• newtonPolytope -- computes the Newton polytope of a polynomial
• normalCone(Polyhedron,Polyhedron) -- computes the normal cone of a face of a polyhedron
• normalFan -- computes the normalFan of a polyhedron
• objectiveVector -- computes an objective vector of a face of a polyhedron
• polar -- computes the polar of a polyhedron
• polarFace -- computes the dual face of the polar polyhedron
• polyhedra -- computes all polyhedra of a polyhedral complex of a certain dimension
• PolyhedralComplex -- the class of all polyhedral complexes
• polyhedralComplex -- generates a PolyhedralComplex
• PolyhedralObject -- the class of all polyhedral objects in Polyhedra
• Polyhedron -- the class of all convex polyhedra
• Polyhedron * Cone -- computes the direct product of a polyhedron and a cone
• Polyhedron * Polyhedron -- computes the direct product of two polyhedra
• Polyhedron + Cone -- computes the Minkowski sum of a polyhedron and a cone
• Polyhedron + Polyhedron -- computes the Minkowski sum of two polyhedra
• polytope -- returns a polytope of which the fan is the normal fan if it is polytopal
• posHull -- computes the positive hull of rays, cones, and the cone over a polyhedron
• posOrthant -- generates the positive orthant in n-space
• proximum -- computes the proximum of the Polyhedron/Cone to a point in euclidian metric
• pyramid -- computes the pyramid over a polyhedron
• QQ * Polyhedron -- rescales a polyhedron by a given positive factor
• rays -- displays all rays of a Cone, a Fan, or a Polyhedron
• saveSession -- save the actual Polyhedra session to a file
• secondaryPolytope -- computes the secondary polytope of a compact polyhedron
• skeleton -- computes the k-skeleton of a Fan or PolyhedralComplex
• smallestFace -- determines the smallest face of the Cone/Polyhedron containing a point
• smoothSubfan -- computes the subfan of all smooth cones
• statePolytope -- computes the state polytope of a homogeneous ideal
• stdSimplex -- generates the d-dimensional standard simplex
• stellarSubdivision -- computes the stellar subdivision of the fan by a ray
• sublatticeBasis -- computes a basis for the sublattice generated by integral vectors or the lattice points of a polytope
• tailCone -- computes the tail/recession cone of a polyhedron
• toSublattice -- calculates the preimage of a polytope in the sublattice generated by its lattice points
• triangulate -- computes a triangulation of a polytope
• vertexEdgeMatrix -- computes the vertex-edge-relations matrix
• vertexFacetMatrix -- computes the vertex-facet-relations matrix
• vertices -- displays the vertices of a Polyhedron or a PolyhedralComplex
• volume -- computes the volume of a polytope