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

Synopsis

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.

See also

Ways to use indexLabeling :

For the programmer

The object indexLabeling is a method function.