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

• Usage:

  Q = dropElements(P, f)

  Q = dropElements(P, L)

  Q = P - L

• Inputs:
  • P, an instance of the type Poset,
  • L, a list, containing elements of $P$ to remove
  • f, a function, which returns true for elements to remove and false otherwise
• Outputs:
  • Q, an instance of the type Poset,

i1 : P = chain 5;

i2 : dropElements(P, {3})

o2 = Relation Matrix: | 1 1 1 1 |
                      | 0 1 1 1 |
                      | 0 0 1 1 |
                      | 0 0 0 1 |

o2 : Poset

i3 : P - {4, 5}

o3 = Relation Matrix: | 1 1 1 |
                      | 0 1 1 |
                      | 0 0 1 |

o3 : Poset

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

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

o5 = Q

o5 : Poset

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

o6 = true