indexLabeling -- relabels a poset with the labeling based on the indices of the vertices

Synopsis

• Usage:
Q = indexLabeling P
• Inputs:
• P, an instance of the type Poset,
• Outputs:
• Q, an instance of the type Poset,

Description

This method simply relabels the ground set of the poset based on the indices of the vertices.

 i1 : P = booleanLattice 3; i2 : Q = indexLabeling P; i3 : P.GroundSet o3 = {000, 001, 010, 011, 100, 101, 110, 111} o3 : List i4 : Q.GroundSet o4 = {0, 1, 2, 3, 4, 5, 6, 7} o4 : List

Clearly, $P$ and $Q$ areIsomorphic.

 i5 : P == Q o5 = true

This can be useful for posets whose vertices have unruly names. Note the cache of $P$ is copied to the cache of $Q$ with the appropriate adjustments being made.