dual(Poset) -- produces the derived poset with relations reversed

Synopsis

Function: dual
Usage:

P' = dual P
Inputs:
- P, an instance of the type Poset,
Outputs:
- P', an instance of the type Poset, the dual of $P$

Description

The dual of a poset is the poset on the same ground set but with all relations reversed.

i1 : P = divisorPoset 12;

i2 : dual P

o2 = Relation Matrix: | 1 0 0 0 0 0 |
                      | 1 1 0 0 0 0 |
                      | 1 0 1 0 0 0 |
                      | 1 1 0 1 0 0 |
                      | 1 1 1 0 1 0 |
                      | 1 1 1 1 1 1 |

o2 : Poset

Clearly then, the chain posets and booleanLattices are all self-dual.

i3 : C = chain 5;

i4 : areIsomorphic(C, dual C)

o4 = true

i5 : B = booleanLattice 4;

i6 : areIsomorphic(B, dual B)

o6 = true