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

Synopsis

Usage:
P' = dual P
Function: dual
Inputs:
- P, an object of class Poset
Outputs:
- P', an object of class 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 = Poset{cache => CacheTable{...6...}                                           }
           GroundSet => {1, 2, 3, 4, 6, 12}
           RelationMatrix => | 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 |
           Relations => {{2, 1}, {3, 1}, {4, 2}, {6, 2}, {6, 3}, {12, 4}, {12, 6}}

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