def random_element(self):
r"""
Return a uniformly random element of ``self``.
ALGORITHM:
This uses the
:meth:`~sage.combinat.posets.posets.FinitePoset.random_order_ideal`
method and the natural bijection with plane partitions.
EXAMPLES::
sage: P = PlanePartitions((4,3,5))
sage: P.random_element()
Plane partition [[4, 3, 3], [4, 0, 0], [2, 0, 0], [0, 0, 0]]
"""
def leq(thing1, thing2):
return all(thing1[i] <= thing2[i] for i in range(len(thing1)))
elem = [(i,j,k) for i in range(self._box[0]) for j in range(self._box[1])
for k in range(self._box[2])]
myposet = Poset((elem, leq))
R = myposet.random_order_ideal()
Z = [[0 for i in range(self._box[1])] for j in range(self._box[0])]
for C in R:
Z[C[0]][C[1]] += 1
return self.element_class(self, Z, check=False)
