CellComplex -- the class of all cell complexes

Functions and methods returning a cell complex :

• cellComplex -- create a cell complex
• cellComplexRPn -- gives a $RP^n$ as a cell complex
• cellComplexSphere -- gives a sphere as a cell complex
• cellComplexTorus -- gives a torus as a cell complex
• hullComplex -- gives the hull complex of a monomial ideal
• relabelCellComplex -- relabels a cell complex
• scarfComplex -- gives the hull complex of a monomial ideal
• skeleton(ZZ,CellComplex) -- computes the $r$-skeleton of a cell complex
• subcomplex -- the subcomplex induced by a degree or monomial
• taylorComplex -- gives the Taylor complex of a monomial ideal

Methods that use a cell complex :

• boundaryMap(ZZ,CellComplex) -- compute the boundary map of a cell complex from r-faces to (r-1)-faces
• cells(CellComplex) -- see cells -- return the cells of a cell complex as a hashtable whose keys are cell dimensions
• cells(ZZ,CellComplex) -- return the cells of a cell complex
• chainComplex(CellComplex) -- compute the cellular chain complex for a cell complex
• dim(CellComplex) -- compute the dimension of a cell complex
• facePoset(CellComplex) -- generates the face poset of a cell complex
• HH CellComplex -- compute the homology modules of a cell complex
• HH^ZZ CellComplex -- cohomology of a cell complex
• HH_ZZ CellComplex -- compute the homology modules of a cell complex
• isFree(CellComplex) -- see isFree -- checks if the labels of a cell complex are free modules
• isMinimal(CellComplex) -- see isMinimal -- check if a labeled cell complex supports a minimal resolution
• isWellDefined(CellComplex) -- checks if a cell complex is well defined
• maxCells(CellComplex) -- see maxCells -- gives the maximal cells of a cell complex
• net(CellComplex) (missing documentation)
• relabelCellComplex(CellComplex,HashTable) -- see relabelCellComplex -- relabels a cell complex
• ring(CellComplex) -- return the base ring of a cell complex
• RingMap ** CellComplex -- tensors labels via a ring map
• CellComplex _ List -- see subcomplex -- the subcomplex induced by a degree or monomial
• CellComplex _ RingElement -- see subcomplex -- the subcomplex induced by a degree or monomial
• CellComplex _ ZZ -- see subcomplex -- the subcomplex induced by a degree or monomial
• subcomplex(CellComplex,List) -- see subcomplex -- the subcomplex induced by a degree or monomial
• subcomplex(CellComplex,RingElement) -- see subcomplex -- the subcomplex induced by a degree or monomial
• subcomplex(CellComplex,ZZ) -- see subcomplex -- the subcomplex induced by a degree or monomial

For the programmer

The object CellComplex is a type, with ancestor classes HashTable < Thing.