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Posets :: dual(Poset)

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

Synopsis

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