hasseDiagram -- produces the Hasse diagram of a poset

Synopsis

• Usage:

  D = hasseDiagram P

• Inputs:

  • P, an object of class Poset
• Outputs:

  • 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

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

See also

• coveringRelations -- computes the minimal list of generating relations of a poset