CellularResolutions : Table of Contents

• CellularResolutions -- A package for cellular resolutions of monomial ideals
• boundary -- returns the boundary cells along with relative orientations
• boundaryCells -- returns the boundary cells of the given cell
• boundaryMap(ZZ,CellComplex) -- compute the boundary map of a cell complex from r-faces to (r-1)-faces
• Cell -- the class of all cells in cell complexes
• CellComplex -- the class of all cell complexes
• cellComplex -- create a cell complex
• cellComplex(Ring,PolyhedralComplex) -- creates cell complex from given polyhedral complex
• cellComplex(Ring,Polyhedron) -- creates cell complex from given polyhedron
• cellComplex(Ring,SimplicialComplex) -- Creates a cell complex from a given simplicial 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
• cellLabel -- return the label of a cell
• 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
• complex(CellComplex) -- compute the cellular chain complex for a cell complex
• dim(Cell) -- compute the dimension of a cell
• 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
• hullComplex -- gives the hull complex of a monomial ideal
• isCycle -- checks if a list of cells with orientation make a cycle
• isFree(CellComplex) -- checks if the labels of a cell complex are free modules
• isMinimal -- check if a labeled cell complex supports a minimal resolution
• isSimplex -- check if a cell is a simplex
• isWellDefined(Cell) -- checks if a cell is well defined
• isWellDefined(CellComplex) -- checks if a cell complex is well defined
• maxCells -- gives the maximal cells of a cell complex
• newCell -- creates a new cell
• newSimplexCell -- create a new cell
• relabelCellComplex -- relabels a cell complex
• ring(CellComplex) -- return the base ring of a cell complex
• RingMap ** CellComplex -- tensors labels via a ring map
• 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