-- -*- M2-comint -*- hash: 11130803806583976164

i1 : setPrecompute true;

i2 : C = chain 10;

i3 : peek C.cache

o3 = CacheTable{connectedComponents => {{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}}                                      }
                coveringRelations => {{0, 1}, {1, 2}, {2, 3}, {3, 4}, {4, 5}, {5, 6}, {6, 7}, {7, 8}, {8, 9}}
                filtration => {{0}, {1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}, {9}}
                greeneKleitmanPartition => Partition{10}
                isAtomic => false
                isDistributive => true
                isEulerian => false
                isLowerSemilattice => true
                isLowerSemimodular => true
                isUpperSemilattice => true
                isUpperSemimodular => true
                maximalAntichains => {{0}, {1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}, {9}}
                maximalChains => {{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}}
                maximalElements => {9}
                minimalElements => {0}
                name => C
                rankFunction => {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

i4 : P = poset apply(9, i -> {i+1, i+2});

i5 : peek P.cache

o5 = CacheTable{name => P}

i6 : C == P

o6 = true

i7 : time isDistributive C
 -- used 7.131e-06s (cpu); 5.209e-06s (thread); 0s (gc)

o7 = true

i8 : time isDistributive P
 -- used 5.45388s (cpu); 4.10318s (thread); 0s (gc)

o8 = true

i9 : C' = dual C;

i10 : time isDistributive C'
 -- used 4.44e-06s (cpu); 3.99e-06s (thread); 0s (gc)

o10 = true

i11 : peek C'.cache

o11 = CacheTable{connectedComponents => {{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}}                                      }
                 coveringRelations => {{1, 0}, {2, 1}, {3, 2}, {4, 3}, {5, 4}, {6, 5}, {7, 6}, {8, 7}, {9, 8}}
                 filtration => {{9}, {8}, {7}, {6}, {5}, {4}, {3}, {2}, {1}, {0}}
                 greeneKleitmanPartition => Partition{10}
                 isDistributive => true
                 isEulerian => false
                 isLowerSemilattice => true
                 isLowerSemimodular => true
                 isUpperSemilattice => true
                 isUpperSemimodular => true
                 maximalAntichains => {{0}, {1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}, {9}}
                 maximalChains => {{9, 8, 7, 6, 5, 4, 3, 2, 1, 0}}
                 maximalElements => {0}
                 minimalElements => {9}
                 name => C'
                 rankFunction => {9, 8, 7, 6, 5, 4, 3, 2, 1, 0}

i12 : 
