Many routines in this package are written to take advantage of known structure on some posets to quickly precompute some of the cached data. However, this may not always be desirable, and so this flag toggles whether precomputation occurs. It can be set with the setPrecompute method.
As an example, chain posets are known to be distributive lattices. If the precomputation flag is set, then the method fills this in automatically.
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 3.039e-6 seconds
o7 = true
|
i8 : time isDistributive P
-- used 2.30812 seconds
o8 = true
|
We also know that the dual of a distributive lattice is again a distributive lattice. Other information is copied when possible.
i9 : C' = dual C; |
i10 : time isDistributive C'
-- used 2.814e-6 seconds
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}
|
The object Precompute is a symbol.