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asked 2 years ago

klaaa gravatar image

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 ba, then bI 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