ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 16 Jul 2023 19:08:18 +0200Obtaining the posets of ideals of a given finite posethttps://ask.sagemath.org/question/70261/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 helpSun, 16 Jul 2023 19:08:18 +0200https://ask.sagemath.org/question/70261/obtaining-the-posets-of-ideals-of-a-given-finite-poset/