# 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