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.
The object indexLabeling is a method function.