Section 9.2 Tables of Operations
This section examines the representation of meet \((∧)\) and join \((∨)\) operations within lattices using operation tables.
Subsection 9.2.1 Meet Operation Table
The meet operation table illustrates the greatest lower bound, or meet, for every pair of elements in the lattice.
To output the table as a matrix, we need to specify that the poset is indeed a lattice, thus requiring us to use the function
LatticePoset(). Then, we can use the function meet_matrix() to process the table.From the output matrix, we can see that each entry \(a_{ij}\) is not the actual value of the meet of the elements \(a_{i}\) and \(a_{j}\) but just its position in the lattice. Let’s show the values:
Show the output as a table:
Subsection 9.2.2 Join Operation Table
Conversely, the join operation table presents the least upper bound, or join, for each pair of lattice elements.
Output the elements of the poset:
Show the output as a table instead of a matrix.
