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CellularResolutions : Index
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boundary
-- returns the boundary cells along with relative orientations
boundary(Cell)
-- returns the boundary cells along with relative orientations
boundaryCells
-- returns the boundary cells of the given cell
boundaryCells(Cell)
-- 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 _ List
-- the subcomplex induced by a degree or monomial
CellComplex _ RingElement
-- the subcomplex induced by a degree or monomial
CellComplex _ ZZ
-- the subcomplex induced by a degree or monomial
cellComplex(Ring,List)
-- create a cell complex
cellComplex(Ring,PolyhedralComplex)
-- creates cell complex from given polyhedral complex
cellComplex(Ring,PolyhedralComplex,Labels=>...)
-- creates cell complex from given polyhedral complex
cellComplex(Ring,Polyhedron)
-- creates cell complex from given polyhedron
cellComplex(Ring,Polyhedron,Labels=>...)
-- creates cell complex from given polyhedron
cellComplex(Ring,SimplicialComplex)
-- Creates a cell complex from a given simplicial complex
cellComplex(Ring,SimplicialComplex,Labels=>...)
-- Creates a cell complex from a given simplicial complex
cellComplexRPn
-- gives a $RP^n$ as a cell complex
cellComplexRPn(Ring,ZZ)
-- gives a $RP^n$ as a cell complex
cellComplexSphere
-- gives a sphere as a cell complex
cellComplexSphere(Ring,ZZ)
-- gives a sphere as a cell complex
cellComplexTorus
-- gives a torus as a cell complex
cellComplexTorus(Ring,ZZ)
-- gives a torus as a cell complex
CellDimension
-- creates a new cell
cellLabel
-- return the label of a cell
cellLabel(Cell)
-- return the label of a cell
cells
-- return the cells of a cell complex as a hashtable whose keys are cell dimensions
cells(CellComplex)
-- 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
CellularResolutions
-- A package for cellular resolutions of monomial ideals
complex(CellComplex)
-- compute the cellular chain complex for a cell complex
complex(CellComplex,Prune=>...)
-- compute the cellular chain complex for a cell complex
complex(CellComplex,Reduced=>...)
-- 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
hullComplex(MonomialIdeal)
-- gives the hull complex of a monomial ideal
hullComplex(QQ,MonomialIdeal)
-- gives the hull complex of a monomial ideal
hullComplex(ZZ,MonomialIdeal)
-- gives the hull complex of a monomial ideal
InferLabels
-- relabels a cell complex
isCycle
-- checks if a list of cells with orientation make a cycle
isCycle(List)
-- 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
isMinimal(CellComplex)
-- check if a labeled cell complex supports a minimal resolution
isSimplex
-- check if a cell is a simplex
isSimplex(Cell)
-- 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
LabelRing
-- the subcomplex induced by a degree or monomial
maxCells
-- gives the maximal cells of a cell complex
maxCells(CellComplex)
-- gives the maximal cells of a cell complex
newCell
-- creates a new cell
newCell(...,CellDimension=>...)
-- creates a new cell
newCell(List)
-- creates a new cell
newCell(List,Ideal)
-- creates a new cell
newCell(List,Module)
-- creates a new cell
newCell(List,Number)
-- creates a new cell
newCell(List,RingElement)
-- creates a new cell
newSimplexCell
-- create a new cell
newSimplexCell(List)
-- create a new cell
newSimplexCell(List,Ideal)
-- create a new cell
newSimplexCell(List,Module)
-- create a new cell
newSimplexCell(List,Number)
-- create a new cell
newSimplexCell(List,RingElement)
-- create a new cell
Reduced
-- compute the cellular chain complex for a cell complex
relabelCellComplex
-- relabels a cell complex
relabelCellComplex(...,InferLabels=>...)
-- relabels a cell complex
relabelCellComplex(CellComplex,HashTable)
-- 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
scarfComplex(MonomialIdeal)
-- 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
subcomplex(...,LabelRing=>...)
-- the subcomplex induced by a degree or monomial
subcomplex(CellComplex,List)
-- the subcomplex induced by a degree or monomial
subcomplex(CellComplex,RingElement)
-- the subcomplex induced by a degree or monomial
subcomplex(CellComplex,ZZ)
-- the subcomplex induced by a degree or monomial
taylorComplex
-- gives the Taylor complex of a monomial ideal
taylorComplex(MonomialIdeal)
-- gives the Taylor complex of a monomial ideal