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.Sat, 10 Oct 2020 14:01:56 +0200Obtaining certain minimal elements for latticeshttps://ask.sagemath.org/question/53804/obtaining-certain-minimal-elements-for-lattices/Let $L$ be a finite lattice and $L^{op}$ the opposite lattice. We can then look at the product lattice $U=L^{op} \times L$ and inside $U$ the poset $S_L=$ { $ (r_1,r_2 ) \in L^{op} \times L | r_2 \nleq r_1 $ }.
My question is whether there is an easy way to obtain the poset $S_L$ for a given lattice $L$ together with the minimal elements $min(S_L)$ of $S_L$.Fri, 09 Oct 2020 16:41:50 +0200https://ask.sagemath.org/question/53804/obtaining-certain-minimal-elements-for-lattices/Answer by FrédéricC for <p>Let $L$ be a finite lattice and $L^{op}$ the opposite lattice. We can then look at the product lattice $U=L^{op} \times L$ and inside $U$ the poset $S_L=$ { $ (r_1,r_2 ) \in L^{op} \times L | r_2 \nleq r_1 $ }.
My question is whether there is an easy way to obtain the poset $S_L$ for a given lattice $L$ together with the minimal elements $min(S_L)$ of $S_L$.</p>
https://ask.sagemath.org/question/53804/obtaining-certain-minimal-elements-for-lattices/?answer=53807#post-id-53807Like this maybe
sage: L = posets.TamariLattice(2)
sage: U = L.dual() * L
sage: S = U.subposet((x,y) for x,y in U if not L.le(y,x))Sat, 10 Oct 2020 12:40:08 +0200https://ask.sagemath.org/question/53804/obtaining-certain-minimal-elements-for-lattices/?answer=53807#post-id-53807Comment by klaaa for <p>Like this maybe</p>
<pre><code>sage: L = posets.TamariLattice(2)
sage: U = L.dual() * L
sage: S = U.subposet((x,y) for x,y in U if not L.le(y,x))
</code></pre>
https://ask.sagemath.org/question/53804/obtaining-certain-minimal-elements-for-lattices/?comment=53812#post-id-53812Thank you very much. My guess for general lattices was wrong, so I deleted it.Sat, 10 Oct 2020 14:01:56 +0200https://ask.sagemath.org/question/53804/obtaining-certain-minimal-elements-for-lattices/?comment=53812#post-id-53812