hasseDiagram -- produces the Hasse diagram of a poset

Synopsis

Usage:

D = hasseDiagram P
Inputs:
- P, an instance of the type Poset,
Outputs:
- D, an instance of the type Digraph, which has the direct edge $(a,b)$ if and only if $a < b$ in $P$ and if $a \leq c \leq b$ 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 => {1, 2, 4}}
             1 => {3, 5}
             2 => {3, 6}
             3 => {7}
             4 => {5, 6}
             5 => {7}
             6 => {7}
             7 => {}

o1 : Digraph

Caveat

This method renames the vertices with integers $0, 1, \ldots$ corresponding to the index of the vertices in the GroundSet.

Ways to use `hasseDiagram` :

"hasseDiagram(Poset)"

For the programmer

The object hasseDiagram is a method function.