CellularResolutions : Index
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boundary -- returns the boundary cells along with relative orientations
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boundary(Cell) -- returns the boundary cells along with relative orientations
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boundaryCells -- returns the boundary cells of the given cell
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boundaryCells(Cell) -- returns the boundary cells of the given cell
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boundaryMap(ZZ,CellComplex) -- compute the boundary map of a cell complex from r-faces to (r-1)-faces
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Cell -- the class of all cells in cell complexes
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CellComplex -- the class of all cell complexes
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cellComplex -- create a cell complex
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CellComplex _ List -- the subcomplex induced by a degree or monomial
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CellComplex _ RingElement -- the subcomplex induced by a degree or monomial
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CellComplex _ ZZ -- the subcomplex induced by a degree or monomial
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cellComplex(Ring,List) -- create a cell complex
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cellComplex(Ring,PolyhedralComplex) -- creates cell complex from given polyhedral complex
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cellComplex(Ring,PolyhedralComplex,Labels=>...) -- creates cell complex from given polyhedral complex
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cellComplex(Ring,Polyhedron) -- creates cell complex from given polyhedron
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cellComplex(Ring,Polyhedron,Labels=>...) -- creates cell complex from given polyhedron
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cellComplex(Ring,SimplicialComplex) -- Creates a cell complex from a given simplicial complex
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cellComplex(Ring,SimplicialComplex,Labels=>...) -- Creates a cell complex from a given simplicial complex
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cellComplexRPn -- gives a $RP^n$ as a cell complex
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cellComplexRPn(Ring,ZZ) -- gives a $RP^n$ as a cell complex
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cellComplexSphere -- gives a sphere as a cell complex
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cellComplexSphere(Ring,ZZ) -- gives a sphere as a cell complex
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cellComplexTorus -- gives a torus as a cell complex
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cellComplexTorus(Ring,ZZ) -- gives a torus as a cell complex
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CellDimension -- creates a new cell
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cellLabel -- return the label of a cell
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cellLabel(Cell) -- return the label of a cell
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cells -- return the cells of a cell complex as a hashtable whose keys are cell dimensions
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cells(CellComplex) -- return the cells of a cell complex as a hashtable whose keys are cell dimensions
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cells(ZZ,CellComplex) -- return the cells of a cell complex
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CellularResolutions -- A package for cellular resolutions of monomial ideals
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chainComplex(CellComplex) -- compute the cellular chain complex for a cell complex
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chainComplex(CellComplex,Prune=>...) -- compute the cellular chain complex for a cell complex
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chainComplex(CellComplex,Reduced=>...) -- compute the cellular chain complex for a cell complex
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dim(Cell) -- compute the dimension of a cell
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dim(CellComplex) -- compute the dimension of a cell complex
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facePoset(CellComplex) -- generates the face poset of a cell complex
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HH CellComplex -- compute the homology modules of a cell complex
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HH^ZZ CellComplex -- cohomology of a cell complex
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HH_ZZ CellComplex -- compute the homology modules of a cell complex
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hullComplex -- gives the hull complex of a monomial ideal
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hullComplex(MonomialIdeal) -- gives the hull complex of a monomial ideal
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hullComplex(QQ,MonomialIdeal) -- gives the hull complex of a monomial ideal
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hullComplex(ZZ,MonomialIdeal) -- gives the hull complex of a monomial ideal
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InferLabels -- relabels a cell complex
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isCycle -- checks if a list of cells with orientation make a cycle
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isCycle(List) -- checks if a list of cells with orientation make a cycle
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isFree -- checks if the labels of a cell complex are free modules
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isFree(CellComplex) -- checks if the labels of a cell complex are free modules
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isMinimal -- check if a labeled cell complex supports a minimal resolution
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isMinimal(CellComplex) -- check if a labeled cell complex supports a minimal resolution
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isSimplex -- check if a cell is a simplex
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isSimplex(Cell) -- check if a cell is a simplex
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isWellDefined(Cell) -- checks if a cell is well defined
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isWellDefined(CellComplex) -- checks if a cell complex is well defined
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LabelRing -- the subcomplex induced by a degree or monomial
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maxCells -- gives the maximal cells of a cell complex
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maxCells(CellComplex) -- gives the maximal cells of a cell complex
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newCell -- creates a new cell
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newCell(...,CellDimension=>...) -- creates a new cell
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newCell(List) -- creates a new cell
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newCell(List,Ideal) -- creates a new cell
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newCell(List,Module) -- creates a new cell
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newCell(List,Number) -- creates a new cell
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newCell(List,RingElement) -- creates a new cell
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newSimplexCell -- create a new cell
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newSimplexCell(List) -- create a new cell
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newSimplexCell(List,Ideal) -- create a new cell
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newSimplexCell(List,Module) -- create a new cell
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newSimplexCell(List,Number) -- create a new cell
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newSimplexCell(List,RingElement) -- create a new cell
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Prune -- compute the cellular chain complex for a cell complex
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Reduced -- compute the cellular chain complex for a cell complex
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relabelCellComplex -- relabels a cell complex
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relabelCellComplex(...,InferLabels=>...) -- relabels a cell complex
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relabelCellComplex(CellComplex,HashTable) -- relabels a cell complex
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ring(CellComplex) -- return the base ring of a cell complex
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RingMap ** CellComplex -- tensors labels via a ring map
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scarfComplex -- gives the hull complex of a monomial ideal
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scarfComplex(MonomialIdeal) -- gives the hull complex of a monomial ideal
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skeleton(ZZ,CellComplex) -- computes the $r$-skeleton of a cell complex
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subcomplex -- the subcomplex induced by a degree or monomial
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subcomplex(...,LabelRing=>...) -- the subcomplex induced by a degree or monomial
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subcomplex(CellComplex,List) -- the subcomplex induced by a degree or monomial
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subcomplex(CellComplex,RingElement) -- the subcomplex induced by a degree or monomial
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subcomplex(CellComplex,ZZ) -- the subcomplex induced by a degree or monomial
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taylorComplex -- gives the Taylor complex of a monomial ideal
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taylorComplex(MonomialIdeal) -- gives the Taylor complex of a monomial ideal