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Posets :: distributiveLattice

distributiveLattice -- computes the lattice of order ideals of a poset

Synopsis

Description

The distributive lattice of a poset P is the poset of all order ideals of P ordered by inclusion.
i1 : P = poset {{1,2}, {1,3}};
i2 : distributiveLattice P

o2 = Poset{cache => CacheTable{...4...}                                                                                                                                   }
           GroundSet => {{}, {1}, {1, 2}, {1, 3}, {1, 2, 3}}
           RelationMatrix => | 1 1 1 1 1 |
                             | 0 1 1 1 1 |
                             | 0 0 1 0 1 |
                             | 0 0 0 1 1 |
                             | 0 0 0 0 1 |
           Relations => {{{}, {1}}, {{}, {1, 2}}, {{}, {1, 3}}, {{}, {1, 2, 3}}, {{1}, {1, 2}}, {{1}, {1, 3}}, {{1}, {1, 2, 3}}, {{1, 2}, {1, 2, 3}}, {{1, 3}, {1, 2, 3}}}

o2 : Poset
The distributive lattice of a chain poset of length n is the chain poset of length n+1.
i3 : distributiveLattice chain 3

o3 = Poset{cache => CacheTable{...4...}                                                                                 }
           GroundSet => {{}, {1}, {1, 2}, {1, 2, 3}}
           RelationMatrix => | 1 1 1 1 |
                             | 0 1 1 1 |
                             | 0 0 1 1 |
                             | 0 0 0 1 |
           Relations => {{{}, {1}}, {{}, {1, 2}}, {{}, {1, 2, 3}}, {{1}, {1, 2}}, {{1}, {1, 2, 3}}, {{1, 2}, {1, 2, 3}}}

o3 : Poset

See also

Ways to use distributiveLattice :