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 = Relation Matrix: | 1 1 1 1 1 | | 0 1 1 1 1 | | 0 0 1 1 0 | | 0 0 0 1 0 | | 0 0 0 1 1 | 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 = Relation Matrix: | 1 1 1 1 | | 0 1 1 1 | | 0 0 1 1 | | 0 0 0 1 | o3 : Poset |
The object distributiveLattice is a method function.