facePoset(CellComplex) -- generates the face poset of a cell complex

Synopsis

Function: facePoset
Usage:

facePoset C
Inputs:
- C, a cell complex,
Outputs:
- an instance of the type Poset, the face poset of C

Description

The face poset of a cell complex is the poset of cells with partial ordering given by inclusion. The example below constructs the square as a cellular complex and returns the face poset.

i1 : R = QQ;

i2 : v1 = newCell {};

i3 : v2 = newCell {};

i4 : v3 = newCell {};

i5 : v4 = newCell {};

i6 : e12 = newCell({v1,v2});

i7 : e23 = newCell({v2,v3});

i8 : e34 = newCell({v3,v4});

i9 : e41 = newCell({v4,v1});

i10 : f = newCell({e12,e23,e34,e41});

i11 : C = cellComplex(R,{f});

i12 : facePoset C

o12 = Relation Matrix: | 1 0 0 0 1 0 1 0 1 |
                       | 0 1 0 0 0 0 1 1 1 |
                       | 0 0 1 0 0 1 0 1 1 |
                       | 0 0 0 1 1 1 0 0 1 |
                       | 0 0 0 0 1 0 0 0 1 |
                       | 0 0 0 0 0 1 0 0 1 |
                       | 0 0 0 0 0 0 1 0 1 |
                       | 0 0 0 0 0 0 0 1 1 |
                       | 0 0 0 0 0 0 0 0 1 |

o12 : Poset

Ways to use this method: