A cell complex in this context is the combinatorial data of a CW-complex, i.e. a collection of cells in various dimensions along with their boundary expressed as a sequence of cells along with an orientation such that the boundary is a cycle.

Not every object represented by a `CellComplex`

object corresponds to a topological cell complex. In general there is no way to check that such a topological realization exists.

- Cell -- the class of all cells in cell complexes

- 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

- 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

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