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# OldPolyhedra : Index

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

- 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(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