- Introduction and First Examples
- Polytopes, Cones and Polyhedra
- Polytopes
- Polytope(Q) : SeqEnum -> TorPol
- PolyhedronWithInequalities(A,c) : SeqEnum,[RngIntElt] -> TorPol
- RandomPolytope(L,n,k) : TorLat,RngIntElt,RngIntElt -> TorPol
- BoundingBox(P) : TorPol -> TorPol,TorLatElt,TorLatElt
- Polar(P) : TorPol -> TorPol
- CrossPolytope(L) : TorLat -> TorPol
- StandardSimplex(L) : TorLat -> TorPol
- CyclicPolytope(L,n) : TorLat,RngIntElt -> TorPol
- PolytopeOfProjectiveSpace(d) : RngIntElt -> TorPol
- PolytopeOfWPS(W) : [RngIntElt] -> TorPol
- Cones
- Cone(A) : Seq -> TorCon
- Cone(v) : TorLatElt -> TorCon
- ConeWithInequalities(B) : Set -> TorCon
- FullCone(L): TorLat -> TorCon
- PositiveQuadrant(L) : TorLat -> TorCon
- ZeroCone(L): TorLat -> TorCon
- RandomCone(d,n,k) : RngIntElt,RngIntElt,RngIntElt -> TorCon
- RandomPositiveCone(d,n,k) : RngIntElt,RngIntElt,RngIntElt -> TorCon
- Dual(C): TorCon -> TorCon
- NormalisedCone(P) : TorPol -> TorCon
- ConeInSublattice(C) : TorCon -> TorCon,Map
- ConeQuotientByLinearSubspace(C) : TorCon -> TorCon,Map,Map
- SimplicialSubcone(C) : TorCon -> TorCon
- LatticeBasisInCone(C) : TorCon -> [TorLatElt]
- Polyhedra
- Polyhedron(C,H,h) : TorCon,TorLatElt,FldRatElt -> TorPol
- Polyhedron(C) : TorCon -> TorPol
- HalfspaceToPolyhedron(v,h) : TorLatElt,FldRatElt -> TorPol
- HyperplaneToPolyhedron(v,h) : TorLatElt,FldRatElt -> TorPol
- Polyhedron(C,f,v) : TorCon,Map,TorLatElt -> TorPol
- EmptyPolyhedron(L) : TorLat -> TorPol
- ConeToPolyhedron(C) : TorCon -> TorPol
- PolyhedronInSublattice(P) : TorPol -> TorPol,Map,TorLatElt
- FixedSubspaceToPolyhedron(G) : GrpMat -> TorPol
- Example Polyhedra_toric-polyhedron-example (H152E3)
- Arithmetic Operations on Polyhedra
- Basic Combinatorics of Polytopes and Polyhedra
- Vertices and Inequalities
- Facets and Faces
- [Future release] fVector(C) : TorCon -> SeqEnum[RngIntElt]
- [Future release] hVector(C) : TorCon -> SeqEnum[RngIntElt]
- Facets(C) : TorCon -> SeqEnum
- FacetIndices(P) : TorPol -> SeqEnum
- NumberOfFacets(P) : TorPol -> RngIntElt
- Faces(C) : TorCon -> SeqEnum
- FaceIndices(P,i) : TorPol,RngIntElt -> SeqEnum
- NumberOfFaces(P,i) : TorPol,RngIntElt -> RngIntElt
- Edges(P) : TorPol -> SeqEnum
- EdgeIndices(P) : TorPol -> SeqEnum
- NumberOfEdges(P) : TorPol -> RngIntElt
- Graph(P) : TorPol -> GrphUnd
- FaceSupportedBy(C,H) : TorCon,TorLatElt -> TorCon
- IsSupportingHyperplane(v,h,P) : TorLatElt,FldRatElt,TorPol -> BoolElt,RngIntElt
- SupportingCone(P,v) : TorPol,TorLatElt -> TorCon
- IsFace(C,F) : TorCon,TorCon -> BoolElt
- The Combinatorics of Polytopes
- Cones and Polyhedra
- Toric Lattices
- Toric Lattices
- Points of Toric Lattices
- L ! [a,b,...] : TorLat,[RngIntElt] -> TorLatElt
- L . i : TorLat,RngIntElt -> TorLatElt
- Basis(L) : TorLat -> TorLatElt
- Form(L,Q) : TorLat,[RngIntElt] -> TorLatElt
- Zero(L) : TorLat -> TorLatElt
- P + Q : TorLatElt,TorLatElt -> TorLatElt
- P eq Q : TorLatElt,TorLatElt -> BoolElt
- AreProportional(P,Q) : TorLatElt,TorLatElt -> BoolElt, FldRatElt
- P / Q : TorLatElt,TorLatElt -> FldRatElt
- Example Polyhedra_toric-example-pt (H152E18)
- v in L : TorLatElt,TorLat -> BoolElt
- Matrix(R,S) : Rng, [TorLatElt] -> ModMatRngElt
- Vector(v) : TorLatElt -> ModTupFldElt
- IsZero(v) : TorLatElt -> BoolElt
- IsIntegral(v) : TorLatElt -> BoolElt
- IsPrimitive(v) : TorLatElt -> BoolElt
- PrimitiveLatticeVector(v) : TorLatElt -> TorLatElt
- Example Polyhedra_toric-primitive-pt (H152E19)
- Operations on Toric Lattices
- Maps of Toric Lattices
- ZeroMap(L,K) : TorLat,TorLat -> TorLatMap
- IdentityMap(L) : TorLat -> TorLatMap
- hom< L -> K | M > : TorLat,TorLat,Mtrx -> TorLatMap
- LatticeMap(L,Q) : TorLat,[TorLatElt] -> TorLatMap
- DefiningMatrix(f) : TorLatMap -> ModMatRngElt
- Image(f,C) : TorLatMap,TorCon -> TorCon
- Preimage(f,C) : TorLatMap,TorCon -> TorCon
- KernelEmbedding(f) : TorLatMap -> Map
- KernelBasis(f) : TorLatMap -> SeqEnum
- ImageBasis(f) : TorLatMap -> SeqEnum
- IsCokernelTorsionFree(f) : TorLatMap -> BoolElt
- ChangeBasis(v) : TorLatElt -> Map
- Example Polyhedra_toric-change-basis-example (H152E21)
- Bibliography
V2.28, 13 July 2023