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# cellComplex(Ring,SimplicialComplex) -- Creates a cell complex from a given simplicial complex

## Synopsis

• Function: cellComplex
• Usage:
cellComplex(S,D)
• Inputs:
• S, a ring,
• D, , from which the cell complex is created
• Optional inputs:
• Labels => , default value null, that maps simplices represented by monomials to labels
• Outputs:
• , that matches those of the given simplicial complex

## Description

This returns a cellular complex whose faces are those of the given simplicial complex.

 i1 : R = QQ[a..f]; i2 : I = monomialIdeal(a*f, b*d, c*e); o2 : MonomialIdeal of R i3 : Delta = simplicialComplex I; i4 : C = cellComplex(QQ,Delta) o4 = C o4 : CellComplex

The optional parameter Label can be used to provide labels to the resulting cell complex. By default all cells get a label of 1.

 i5 : S = QQ[x,y]; i6 : H = hashTable {a => x^5, b => y*x^4, c=>y^2*x^3, d => y^3*x^2, e => y^4*x, f => x^5}; i7 : C = cellComplex(S,Delta,Labels=>H) o7 = C o7 : CellComplex i8 : applyValues(cells C, l -> apply(l,cellLabel)) 5 4 3 2 2 3 4 5 o8 = HashTable{0 => {x , x y, x y , x y , x*y , x } } 5 3 5 4 5 5 2 5 3 5 4 4 2 4 4 5 3 3 5 2 2 4 1 => {x y , x y , x y, x y , x y , x y , x y , x y , x y, x y , x y , x y } 5 2 5 4 5 3 5 4 5 2 5 4 5 3 5 4 2 => {x y , x y , x y , x y , x y , x y , x y , x y } o8 : HashTable