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Posets :: divisorPoset

divisorPoset -- generates the poset of divisors

Synopsis

Description

The divisor poset of an integer is the poset of positive divisors of an integer n with order induced by divisibility.
i1 : divisorPoset 12

o1 = Poset{cache => CacheTable{...6...}                                           }
           GroundSet => {1, 2, 3, 4, 6, 12}
           RelationMatrix => | 1 1 1 1 1 1 |
                             | 0 1 0 1 1 1 |
                             | 0 0 1 0 1 1 |
                             | 0 0 0 1 0 1 |
                             | 0 0 0 0 1 1 |
                             | 0 0 0 0 0 1 |
           Relations => {{1, 2}, {1, 3}, {2, 4}, {2, 6}, {3, 6}, {4, 12}, {6, 12}}

o1 : Poset
i2 : divisorPoset 30

o2 = Poset{cache => CacheTable{...6...}                                                                                          }
           GroundSet => {1, 2, 3, 5, 6, 10, 15, 30}
           RelationMatrix => | 1 1 1 1 1 1 1 1 |
                             | 0 1 0 0 1 1 0 1 |
                             | 0 0 1 0 1 0 1 1 |
                             | 0 0 0 1 0 1 1 1 |
                             | 0 0 0 0 1 0 0 1 |
                             | 0 0 0 0 0 1 0 1 |
                             | 0 0 0 0 0 0 1 1 |
                             | 0 0 0 0 0 0 0 1 |
           Relations => {{1, 2}, {1, 3}, {1, 5}, {2, 6}, {2, 10}, {3, 6}, {3, 15}, {5, 10}, {5, 15}, {6, 30}, {10, 30}, {15, 30}}

o2 : Poset

See also

Ways to use divisorPoset :