principalOrderIdeal -- computes the elements below a given element in a poset

• Usage:

  I = principalOrderIdeal(P, a)

• Inputs:
  • P, an instance of the type Poset,
  • a, a thing, an element of the poset
• Outputs:
  • I, a list, containing all elements less than or equal to the given elements

i1 : P = booleanLattice 3;

i2 : principalOrderIdeal(P, "101")

o2 = {000, 001, 100, 101}

o2 : List