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

Synopsis

Usage:

L = distributiveLattice P
Inputs:
- P, an instance of the type Poset,
Outputs:
- L, an instance of the type Poset, the distributive lattice of $P$

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 = 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

See also

orderIdeal -- computes the elements below given elements in a poset

Ways to use distributiveLattice :

distributiveLattice(Poset)

For the programmer

The object distributiveLattice is a method function.