chap16.txt

  
  16 Property handlers
  
  As  explained  in  Chapter  5,  objects  of  the  types SCSimplicialComplex,
  SCNormalSurface  and  SCLibRepository provide a set of property handlers for
  ease  of  access  to simpcomp functions using these objects. Accessing these
  property handlers is possible via the .-operator.
  
  For  example,  the  f-vector  of  a simplicial complex c that is stored as a
  SCSimplicialComplex object can be accessed via the statement c.F; instead of
  writing  the  longer  SCFVector(c);.  See below for a list of all properties
  supported  by objects of the types SCPolyhedralComplex, SCSimplicialComplex,
  SCNormalSurface  and  SCLibRepository  (Note  that  the property handlers of
  SCPolyhedralComplex   can   be   used   by   both   SCSimplicialComplex  and
  SCNormalSurface).
  
  
  16.1 Property handlers of SCPolyhedralComplex
  
  This   section   contains   a   table   of   all   property  handlers  of  a
  SCPolyhedralComplex object.
  
        Property handler       Function called               
        ────────────────────     
                                                             
        AntiStar               SCAntiStar (4.3-1)            
        Ast                    SCAntiStar (4.3-1)            
        Facets                 SCFacets (6.9-19)             
        FacetsEx               SCFacetsEx (6.9-20)           
        LabelMax               SCLabelMax (4.2-1)            
        LabelMin               SCLabelMin (4.2-2)            
        Labels                 SCLabels (4.2-3)              
        Lk                     SCLink (4.3-2)                
        Link                   SCLink (4.3-2)                
        Links                  SCLinks (4.3-3)               
        Lks                    SCLinks (4.3-3)               
        Name                   SCName (4.2-4)                
        Reference              SCReference (4.2-5)           
        Relabel                SCRelabel (4.2-6)             
        RelabelStandard        SCRelabelStandard (4.2-7)     
        RelabelTransposition   SCRelabelTransposition (4.2-8)
        Rename                 SCRename (4.2-9)              
        SetReference           SCSetReference (4.2-10)       
  
        Star          SCStar (4.3-4)        
        Str           SCStar (4.3-4)        
        Stars         SCStars (4.3-5)       
        Strs          SCStars (4.3-5)       
        UnlabelFace   SCUnlabelFace (4.2-11)
        Vertices      SCVertices (4.1-3)    
        VerticesEx    SCVerticesEx (4.1-4)  
  
  
  16.2 Property handlers of SCSimplicialComplex
  
  This   section   contains   a   table   of   all   property  handlers  of  a
  SCSimplicialComplex object.
  
        Property handler                Function called                        
        ─────────────────────────────     
                                                                               
        ASDet                           SCAltshulerSteinberg (6.9-1)           
        AlexanderDual                   SCAlexanderDual (6.10-1)               
        AutomorphismGroup               SCAutomorphismGroup (6.9-2)            
        AutomorphismGroupInternal       SCAutomorphismGroupInternal (6.9-3)    
        AutomorphismGroupSize           SCAutomorphismGroupSize (6.9-4)        
        AutomorphismGroupStructure      SCAutomorphismGroupStructure (6.9-5)   
        AutomorphismGroupTransitivity   SCAutomorphismGroupTransitivity (6.9-6)
        Bd                              SCBoundary (6.9-7)                     
        Boundary                        SCBoundary (6.9-7)                     
        BoundaryOperatorMatrix          SCBoundaryOperatorMatrix (8.1-1)       
        Chi                             SCEulerCharacteristic (7.3-3)          
        CoboundaryOperatorMatrix        SCCoboundaryOperatorMatrix (8.2-1)     
        Cohomology                      SCCohomology (8.2-2)                   
        CohomologyBasis                 SCCohomologyBasis (8.2-3)              
        CohomologyBasisAsSimplices      SCCohomologyBasisAsSimplices (8.2-4)   
        CollapseGreedy                  SCCollapseGreedy (12.1-1)              
        Cone                            SCCone (6.10-3)                        
        ConnectedComponents             SCConnectedComponents (7.3-1)          
        Copy                            SCCopy (7.2-1)                         
        CupProduct                      SCCupProduct (8.2-5)                   
        DehnSommervilleCheck            SCDehnSommervilleCheck (6.9-8)         
        DeletedJoin                     SCDeletedJoin (6.10-4)                 
        DetermineTopologicalType        SCLibDetermineTopologicalType (13.1-6) 
        Difference                      SCDifference (6.10-5)                  
        DifferenceCycles                SCDifferenceCycles (6.9-10)            
        Dim                             SCDim (7.3-2)                          
        DualGraph                       SCDualGraph (6.9-12)                   
        Equivalent                      SCEquivalent (9.2-2)                   
        EulerCharacteristic             SCEulerCharacteristic (7.3-3)          
        ExportJavaView                  SCExportJavaView (13.2-9)              
        ExportLatexTable                SCExportLatexTable (13.2-8)            
        ExportPolymake                  SCExportPolymake (13.2-10)             
  
        F                                SCFVector (7.3-4)                       
        FaceLattice                      SCFaceLattice (7.3-5)                   
        FaceLatticeEx                    SCFaceLatticeEx (7.3-6)                 
        Faces                            SCFaces (6.9-17)                        
        FacesEx                          SCFacesEx (6.9-18)                      
        FillSphere                       SCFillSphere (6.10-6)                   
        FpBetti                          SCFpBettiNumbers (7.3-7)                
        FundamentalGroup                 SCFundamentalGroup (6.9-22)             
        G                                SCGVector (6.9-23)                      
        Generators                       SCGenerators (6.9-24)                   
        GeneratorsEx                     SCGeneratorsEx (6.9-25)                 
        H                                SCHVector (6.9-26)                      
        HandleAddition                   SCHandleAddition (6.10-7)               
        HasBd                            SCHasBoundary (6.9-27)                  
        HasBoundary                      SCHasBoundary (6.9-27)                  
        HasInt                           SCHasInterior (6.9-28)                  
        HasInterior                      SCHasInterior (6.9-28)                  
        HasseDiagram                     SCHasseDiagram (12.1-4)                 
        Homology                         SCHomology (12.1-12)                    
        HomologyBasis                    SCHomologyBasis (8.1-3)                 
        HomologyBasisAsSimplices         SCHomologyBasisAsSimplices (8.1-4)      
        HomologyInternal                 SCHomologyInternal (8.1-5)              
        Incidences                       SCIncidences (6.9-32)                   
        IncidencesEx                     SCIncidencesEx (6.9-33)                 
        Interior                         SCInterior (6.9-34)                     
        Intersection                     SCIntersection (6.10-8)                 
        IntersectionForm                 SCIntersectionForm (8.2-6)              
        IntersectionFormDimensionality   SCIntersectionFormDimensionality (8.2-8)
        IntersectionFormParity           SCIntersectionFormParity (8.2-7)        
        IntersectionFormSignature        SCIntersectionFormSignature (8.2-9)     
        IsCentrallySymmetric             SCIsCentrallySymmetric (6.9-35)         
        IsConnected                      SCIsConnected (7.3-10)                  
        IsEmpty                          SCIsEmpty (7.3-11)                      
        IsEulerianManifold               SCIsEulerianManifold (6.9-38)           
        IsFlag                           SCIsFlag (6.9-39)                       
        IsHomologySphere                 SCIsHomologySphere (6.9-41)             
        IsInKd                           SCIsInKd (6.9-42)                       
        IsIsomorphic                     SCIsIsomorphic (6.10-9)                 
        IsKNeighborly                    SCIsKNeighborly (6.9-43)                
        IsKStackedSphere                 SCIsKStackedSphere (9.2-5)              
  
        IsManifold                    SCIsManifold (12.1-17)                 
        IsMovable                     SCIsMovableComplex (9.2-7)             
        Isomorphism                   SCIsomorphism (6.10-11)                
        IsomorphismEx                 SCIsomorphismEx (6.10-12)              
        IsOrientable                  SCIsOrientable (7.3-12)                
        IsPM                          SCIsPseudoManifold (6.9-45)            
        IsPure                        SCIsPure (6.9-46)                      
        IsSC                          SCIsSimplyConnected (12.1-14)          
        IsSimplyConnected             SCIsSimplyConnected (12.1-14)          
        IsShellable                   SCIsShellable (6.9-47)                 
        IsSphere                      SCIsSphere (12.1-16)                   
        IsStronglyConnected           SCIsStronglyConnected (6.9-48)         
        IsSubcomplex                  SCIsSubcomplex (6.10-10)               
        IsTight                       SCIsTight (11.1-1)                     
        Join                          SCJoin (6.10-13)                       
        Load                          SCLoad (13.2-1)                        
        MinimalNonFaces               SCMinimalNonFaces (6.9-49)             
        MinimalNonFacesEx             SCMinimalNonFacesEx (6.9-50)           
        MorseIsPerfect                SCMorseIsPerfect (11.1-2)              
        MorseMultiplicityVector       SCMorseMultiplicityVector (11.1-4)     
        MorseNumberOfCriticalPoints   SCMorseNumberOfCriticalPoints (11.1-5) 
        Move                          SCMove (9.2-8)                         
        Moves                         SCMoves (9.2-9)                        
        Neighborliness                SCNeighborliness (6.9-51)              
        Neighbors                     SCNeighbors (6.10-14)                  
        NeighborsEx                   SCNeighborsEx (6.10-15)                
        NumFaces                      SCNumFaces (6.9-52)                    
        Orientation                   SCOrientation (6.9-53)                 
        PropertiesDropped             SCPropertiesDropped (5.1-4)            
        Randomize                     SCRandomize (9.2-11)                   
        RMoves                        SCRMoves (9.2-10)                      
        Reduce                        SCReduceComplex (9.2-13)               
        ReduceAsSubcomplex            SCReduceAsSubcomplex (9.2-12)          
        ReduceEx                      SCReduceComplexEx (9.2-14)             
        Save                          SCSave (13.2-3)                        
        Shelling                      SCShelling (6.10-16)                   
        ShellingExt                   SCShellingExt (6.10-17)                
        Shellings                     SCShellings (6.10-18)                  
        Skel                          SCSkel (7.3-13)                        
        SkelEx                        SCSkelEx (7.3-14)                      
        Slicing                       SCSlicing (11.1-3), SCNSSlicing (7.1-4)
        Span                          SCSpan (6.10-19)                       
        SpanningTree                  SCSpanningTree (6.9-56)                
        StronglyConnectedComponents   SCStronglyConnectedComponents (6.6-9)  
        Suspension                    SCSuspension (6.10-20)                 
        Transitivity                  SCAutomorphismGroupTransitivity (6.9-6)
        Union                         SCUnion (7.3-16)                       
        VertexIdentification          SCVertexIdentification (6.10-22)       
        Wedge                         SCWedge (6.10-23)                      
  
  
  16.3 Property handlers of SCNormalSurface
  
  This  section contains a table of all property handlers of a SCNormalSurface
  object.
  
        Property handler      Function called              
        ───────────────────     
                                                           
        Betti                 SCFpBettiNumbers (7.3-7)     
        ConnectedComponents   SCConnectedComponents (7.3-1)
        FpBettiNumbers        SCFpBettiNumbers (7.3-7)     
        Chi                   SCEulerCharacteristic (7.3-3)
        EulerCharacteristic   SCEulerCharacteristic (7.3-3)
        Connected             SCIsConnected (7.3-10)       
        IsConnected           SCIsConnected (7.3-10)       
        Copy                  SCCopy (7.2-1)               
        D                     SCDim (7.3-2)                
        Dim                   SCDim (7.3-2)                
        F                     SCFVector (7.3-4)            
        FVector               SCFVector (7.3-4)            
        FaceLattice           SCFaceLattice (7.3-5)        
        Faces                 SCSkel (7.3-13)              
        Genus                 SCGenus (7.3-8)              
        Homology              SCHomology (12.1-12)         
        IsEmpty               SCIsEmpty (7.3-11)           
        Name                  SCName (4.2-4)               
        Triangulation         SCNSTriangulation (7.2-2)    
        TopologicalType       SCTopologicalType (7.3-15)   
  
  
  16.4 Property handlers of SCLibRepository
  
  This  section contains a table of all property handlers of a SCLibRepository
  object.
  
        Property handler           Function called                       
        ────────────────────────     
                                                                         
        Update                     SCLibUpdate (13.1-13)                 
        IsLoaded                   SCLibIsLoaded (13.1-9)                
        Size                       SCLibSize (13.1-12)                   
        Status                     SCLibStatus (13.1-14)                 
        Flush                      SCLibFlush (13.1-7)                   
        Add                        SCLibAdd (13.1-3)                     
        Delete                     SCLibDelete (13.1-5)                  
        All                        SCLibAllComplexes (13.1-4)            
        SearchByName               SCLibSearchByName (13.1-11)           
        SearchByAttribute          SCLibSearchByAttribute (13.1-10)      
        DetermineTopologicalType   SCLibDetermineTopologicalType (13.1-6)