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# skeleton(ZZ,CellComplex) -- computes the $r$-skeleton of a cell complex

## Synopsis

• Function: skeleton
• Usage:
skeleton(ZZ,CellComplex)
• Inputs:
• r, an integer, the dimension of the skeleton
• C, , which to take the skeleton of
• Outputs:
• , the $r$-skeleton of the cell complex $C$

## Description

The $r$-skeleton of a cell complex is the union of its cells whose dimension is at most $r$.

 i1 : R = QQ[x]; i2 : P = hypercube 3; i3 : C = cellComplex(R,P); i4 : dim C o4 = 3 i5 : cells C o5 = HashTable{0 => {Cell of dimension 0 with label 1, Cell of dimension 0 with label 1, Cell of dimension 0 with label 1, Cell of dimension 0 with label 1, Cell of dimension 0 with label 1, Cell of dimension 0 with label 1, Cell of dimension 0 with label 1, Cell of dimension 0 with label 1} } 1 => {Cell of dimension 1 with label 1, Cell of dimension 1 with label 1, Cell of dimension 1 with label 1, Cell of dimension 1 with label 1, Cell of dimension 1 with label 1, Cell of dimension 1 with label 1, Cell of dimension 1 with label 1, Cell of dimension 1 with label 1, Cell of dimension 1 with label 1, Cell of dimension 1 with label 1, Cell of dimension 1 with label 1, Cell of dimension 1 with label 1} 2 => {Cell of dimension 2 with label 1, Cell of dimension 2 with label 1, Cell of dimension 2 with label 1, Cell of dimension 2 with label 1, Cell of dimension 2 with label 1, Cell of dimension 2 with label 1} 3 => {Cell of dimension 3 with label 1} o5 : HashTable i6 : S = skeleton(2,C); i7 : dim S o7 = 2 i8 : cells S o8 = HashTable{0 => {Cell of dimension 0 with label 1, Cell of dimension 0 with label 1, Cell of dimension 0 with label 1, Cell of dimension 0 with label 1, Cell of dimension 0 with label 1, Cell of dimension 0 with label 1, Cell of dimension 0 with label 1, Cell of dimension 0 with label 1} } 1 => {Cell of dimension 1 with label 1, Cell of dimension 1 with label 1, Cell of dimension 1 with label 1, Cell of dimension 1 with label 1, Cell of dimension 1 with label 1, Cell of dimension 1 with label 1, Cell of dimension 1 with label 1, Cell of dimension 1 with label 1, Cell of dimension 1 with label 1, Cell of dimension 1 with label 1, Cell of dimension 1 with label 1, Cell of dimension 1 with label 1} 2 => {Cell of dimension 2 with label 1, Cell of dimension 2 with label 1, Cell of dimension 2 with label 1, Cell of dimension 2 with label 1, Cell of dimension 2 with label 1, Cell of dimension 2 with label 1} o8 : HashTable