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, a cell complex, which to take the skeleton of
Outputs:
- a cell complex, 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

Ways to use this method: