The Cartesian product of the posets P and Q is the new poset whose ground set is the Cartesian product of the ground sets of P and Q and with partial order given by (a,b) ≤(c,d) if and only if a ≤c and b ≤d.
i1 : product(chain 3, poset {{a,b},{b,c}})
o1 = Relation Matrix: | 1 1 1 1 1 1 1 1 1 |
| 0 1 1 0 1 1 0 1 1 |
| 0 0 1 0 0 1 0 0 1 |
| 0 0 0 1 1 1 1 1 1 |
| 0 0 0 0 1 1 0 1 1 |
| 0 0 0 0 0 1 0 0 1 |
| 0 0 0 0 0 0 1 1 1 |
| 0 0 0 0 0 0 0 1 1 |
| 0 0 0 0 0 0 0 0 1 |
o1 : Poset
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The product of n chains of length 2 is isomorphic to the boolean lattice on n elements. These are also isomorphic to the divisor lattice on the product of n distinct primes.
i2 : B = booleanLattice 4;
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i3 : B == product(4, i -> chain 2)
o3 = true
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