Lattice of maximum-length antichains in sage

savecancel

Like this

def dilworth(P):
    def lequal(A, B):
        return all(any(P.is_lequal(a, b) for b in B) for a in A)
    w = P.width()
    data = [tuple(a) for a in P.maximal_antichains() if len(a) == w]
    return Poset([data, lequal])

Here is my attempt:

def smallerB(a,B,P):
if len([b for b in B if P.is_lequal(a,b)]) > 0:
    return true
else:
    return false

def smallerP(A,B,P):
      if len(A) == len([a for a in A if smallerB(a,B,P)]):
          return true
      else:
          return false

def dilworth(P):
    ANTI = [Set(_) for _ in P.antichains()]
    maxl = max([len(_) for _ in ANTI])
    MANTI = [_ for _ in ANTI if len(_) == maxl]
    RELS = [[A,B] for A in MANTI for B in MANTI if smallerP(A,B,P)]
    Q = Poset((MANTI, RELS))
    return Q

Now test it:

   P = Poset(([1,2,3,4,5], [[0, 2], [1, 2], [1, 3], [2, 5], [3, 4], [3, 5]]))
   Q = dilworth(P)
   P.plot()
   Q.plot()

I might have misunderstood your definition of the Dilworth lattice, so chek my work!