D, an object of class Digraph, which has the direct edge (a,b) if and only if a < b in P and if a ≤c ≤b then c = a or c = b.
Description
The Hasse diagram of a poset is a Digraph with vertices given by the ground set of P and which has the direct edge (a,b) if and only if a < b in P and there exists no c such that a < c < b.
i1 : hasseDiagram booleanLattice 3
o1 = Digraph{0 => set {1, 2, 4}}
1 => set {3, 5}
2 => set {3, 6}
3 => set {7}
4 => set {5, 6}
5 => set {7}
6 => set {7}
7 => set {}
o1 : Digraph
Caveat
This method renames the vertices with integers 0, 1, ... corresponding to the index of the vertices in the GroundSet.
See also
coveringRelations -- computes the minimal list of generating relations of a poset