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

- 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

## Ways to use this method:

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

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Posets.m2:2635:0.