1
Use R = Posets.RandomPoset(30,0.05)
to construct a random poset. Use R.plot()
to get an idea of what you have built.
Illustrate the use of the poset methods:
.is_lequal()
,.is_less_than()
,.is_gequal()
, and.is_greater_than()
to determine if two specific elements (of your choice) are related or incomparable.Use
.minimal_elements()
and.maximal_elements()
to find the smallest and largest elements of your poset.Use
LatticePoset(R)
to see if the posetR
is a lattice by attempting to convert it into a lattice.Find a linear extension of your poset. Confirm that any pair of elements that are comparable in the poset will be similarly comparable in the linear extension.