Let P be a finite connected poset. Following https://www.jstor.org/stable/2038033 , an ideal I of P is a subset of P with the following two properties:
(1) if a is in I and b≤a, then b∈I and
(2) given any finite subset of elements of I whose join exists in P , the that join is in fact in I.
Question: Is there a quick way to obtain the poset of all ideals of a given poset as a poset in Sage?
Thanks for any help