dropElements -- computes the induced subposet of a poset given a list of elements to remove

i1 : P = chain 5;

i2 : dropElements(P, {3})

o2 = Poset{cache => CacheTable{}                                        }
           GroundSet => {1, 2, 4, 5}
           RelationMatrix => | 1 1 1 1 |
                             | 0 1 1 1 |
                             | 0 0 1 1 |
                             | 0 0 0 1 |
           Relations => {{1, 2}, {1, 4}, {1, 5}, {2, 4}, {2, 5}, {4, 5}}

o2 : Poset

i3 : P - {4, 5}

o3 = Poset{cache => CacheTable{}                }
           GroundSet => {1, 2, 3}
           RelationMatrix => | 1 1 1 |
                             | 0 1 1 |
                             | 0 0 1 |
           Relations => {{1, 2}, {1, 3}, {2, 3}}

o3 : Poset

i4 : P = divisorPoset (2*3*5*7);

i5 : Q = dropElements(P, e -> e % 3 == 0)

o5 = Poset{cache => CacheTable{}                                                                                                                                                                   }
           GroundSet => {1, 2, 5, 7, 10, 14, 35, 70}
           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, 5}, {1, 7}, {1, 10}, {1, 14}, {1, 35}, {1, 70}, {2, 10}, {2, 14}, {2, 70}, {5, 10}, {5, 35}, {5, 70}, {7, 14}, {7, 35}, {7, 70}, {10, 70}, {14, 70}, {35, 70}}

o5 : Poset

i6 : Q == divisorPoset(2*5*7)

o6 = true