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

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

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