10. Property handlers

As explained in chapter 3., an object of type SCSimplicialComplex or SCNormalSurface provides a set of property handlers for easily accessing and computing its properties using the .-operator.
For example, the f-vector of a simplicial complex / normal surface c that is stored as SCSimplicialComplex object can be accessed via the statement c.F;. See below for a list of all properties supported by a SCSimplicialComplex and SCNormalSurface object.

10.1 Property handlers of a SCSimplicialComplex

This section contains a table of all property handlers of a SCSimplicialComplex object.

Property handler Function called
ASDet SCAltshulerSteinberg (4.5-1)
AlexanderDual SCAlexanderDual (4.6-1)
AutomorphismGroup SCAutomorphismGroup (4.5-2)
AutomorphismGroupInternal SCAutomorphismGroupInternal (4.5-3)
Boundary SCBoundary (4.5-4)
BoundaryOperatorMatrix SCBoundaryOperatorMatrix (5.1-1)
Chi SCEulerCharacteristic (4.5-7)
CoboundaryOperatorMatrix SCCoboundaryOperatorMatrix (5.2-1)
Cohomology SCCohomology (5.2-2)
CohomologyBasis SCCohomologyBasis (5.2-3)
CohomologyBasisAsSimplices SCCohomologyBasisAsSimplices (5.2-4)
CollapseGreedy SCCollapseGreedy (4.6-2)
Cone SCCone (4.6-3)
ConnectedComponents SCConnectedComponents (4.3-3)
Copy SCCopy (3.1-2)
CupProduct SCCupProduct (5.2-5)
DeletedJoin SCDeletedJoin (4.6-4)
DetermineTopologicalType SCLibDetermineTopologicalType (8.1-6)
Difference SCDifference (4.6-5)
Dim SCDim (4.5-5)
DualGraph SCDualGraph (4.5-6)
Equivalent SCEquivalent (6.2-2)
ExportJavaView SCExportJavaView (8.2-6)
ExportLatexTable SCExportLatexTable (8.2-5)
ExportPolymake SCExportPolymake (8.2-3)

 


F SCFVector (4.5-8)
FaceLattice SCFaceLattice (4.5-9)
FaceLatticeEx SCFaceLatticeEx (4.5-10)
Faces SCFaces (4.5-11)
FacesEx SCFacesEx (4.5-12)
Facets SCFacets (4.5-13)
FacetsEx SCFacetsEx (4.5-14)
FpBetti SCFpBettiNumbers (4.5-15)
FundamentalGroup SCFundamentalGroup (4.5-16)
G SCGVector (4.5-17)
Generators SCGenerators (4.5-18)
GeneratorsEx SCGeneratorsEx (4.5-19)
H SCHVector (4.5-20)
HandleAddition SCHandleAddition (4.6-6)
HasBoundary SCHasBoundary (4.5-21)
HasInterior SCHasInterior (4.5-22)
Homology SCHomology (4.5-23)
HomologyBasis SCHomologyBasis (5.1-3)
HomologyBasisAsSimplices SCHomologyBasisAsSimplices (5.1-4)
HomologyInternal SCHomologyInternal (5.1-5)
Incidences SCIncidences (4.5-24)
IncidencesEx SCIncidencesEx (4.5-25)
Interior SCInterior (4.5-26)
Intersection SCIntersection (4.6-7)
IntersectionForm SCIntersectionForm (5.2-6)
IntersectionFormDimensionality SCIntersectionFormDimensionality (5.2-8)
IntersectionFormParity SCIntersectionFormParity (5.2-7)
IsCentrallySymmetric SCIsCentrallySymmetric (4.5-27)
IsConnected SCIsConnected (4.5-28)
IsEmpty SCIsEmpty (4.5-29)
IsEulerianManifold SCIsEulerianManifold (4.5-30)
IsHomologySphere SCIsHomologySphere (4.5-31)
IsInKd SCIsInKd (4.5-32)
IsIsomorphic SCIsIsomorphic (4.6-8)
IsKNeighborly SCIsKNeighborly (4.5-33)
IsKStackedSphere SCIsKStackedSphere (6.2-5)
IsManifold SCIsManifold (6.2-6)
IsMovable SCIsMovableComplex (6.2-7)
IsOrientable SCIsOrientable (4.5-34)
IsPM SCIsPseudoManifold (4.5-35)
IsPure SCIsPure (4.5-36)
IsShellable SCIsShellable (4.5-37)
IsStronglyConnected SCIsStronglyConnected (4.5-38)
IsSubcomplex SCIsSubcomplex (4.6-9)
Isomorphism SCIsomorphism (4.6-10)
IsomorphismEx SCIsomorphismEx (4.6-11)

 


Join SCJoin (4.6-12)
LabelMax SCLabelMax (4.4-1)
LabelMin SCLabelMin (4.4-2)
Labels SCLabels (4.4-3)
Link SCLink (4.6-13)
Links SCLinks (4.6-14)
Load SCLoad (8.2-1)
MinimalNonFaces SCMinimalNonFaces (4.5-39)
MinimalNonFacesEx SCMinimalNonFacesEx (4.5-40)
Move SCMove (6.2-8)
Moves SCMoves (6.2-9)
Name SCName (4.5-41)
Neighborliness SCNeighborliness (4.5-42)
Neighbors SCNeighbors (4.6-15)
NeighborsEx SCNeighborsEx (4.6-16)
NumFaces SCNumFaces (4.5-43)
Orientation SCOrientation (4.5-44)
RMoves SCRMoves (6.2-10)
Recalc SCForceRecalc (3.1-4)
Reduce SCReduceComplex (6.2-12)
ReduceAsSubcomplex SCReduceAsSubcomplex (6.2-11)
ReduceEx SCReduceComplexEx (6.2-13)
Relabel SCRelabel (4.4-4)
RelabelStandard SCRelabelStandard (4.4-5)
RelabelTransposition SCRelabelTransposition (4.4-6)
Rename SCRename (4.4-7)
Save SCSave (8.2-2)
Shelling SCShelling (4.6-17)
ShellingExt SCShellingExt (4.6-18)
Shellings SCShellings (4.6-19)
Skel SCSkel (4.5-45)
SkelEx SCSkelEx (4.5-46)
Slicing SCNSSlicing (7.1-4)
SortComplex SCSortComplex (4.4-8)
Span SCSpan (4.6-20)
SpanningTree SCSpanningTree (4.5-47)
Star SCStar (4.6-21)
Stars SCStars (4.6-22)
StronglyConnectedComponents SCStronglyConnectedComponents (4.3-11)
Suspension SCSuspension (4.6-23)
Union SCUnion (4.6-24)
UnlabelFace SCUnlabelFace (4.4-9)
VertexIdentification SCVertexIdentification (4.6-25)
Vertices SCVertices (4.5-48)
VerticesEx SCVerticesEx (4.5-49)
Wedge SCWedge (4.6-26)

 


10.2 Property handlers of a SCNormalSurface

This section contains a table of all property handlers of a SCNormalSurface object.

Property handler Function called
Betti SCNSFpBettiNumbers
Chi SCNSEulerCharacteristic
ConnComp SCConnectedComponents
Connected SCIsConnected
Copy SCNSCopy
Dim SCNSDim
F SCNSFVector
FaceLattice SCNSFaceLattice
Faces SCNSSkel
Facets SCFacets
Genus SCNSGenus
Homology SCNSHomology
IsEmpty SCIsEmpty
Labels SCLabels
Name SCName
Triangulation SCNSSubdivision
Type SCNSTopologicalType
Vertices SCVertices

 





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