OldPolyhedra : Index

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