# Obtaining the posets of ideals of a given finite poset

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 $b \leq a$, then $b \in I$ 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