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.Tue, 22 Sep 2020 12:29:10 +0200Obtaining a group from distributive latticeshttps://ask.sagemath.org/question/53455/obtaining-a-group-from-distributive-lattices/Let $P$ be a finite lattice with incidence algebra $I(P,K)$ over a field $K$.
A function $f$ in $I(P,K)$ is called strongly multiplicative if $f(x \land y , x \lor y)=f(x \land y, x) f(x \land y ,y )$ for all $x,y \in P$. $P$ is distributive if and only if the strongly multiplicative invertible functions form a group.
My question is whether there is an easy way to obtain this group using Sage for a given $P$.Mon, 14 Sep 2020 18:29:47 +0200https://ask.sagemath.org/question/53455/obtaining-a-group-from-distributive-lattices/Comment by dan_fulea for <p>Let $P$ be a finite lattice with incidence algebra $I(P,K)$ over a field $K$.
A function $f$ in $I(P,K)$ is called strongly multiplicative if $f(x \land y , x \lor y)=f(x \land y, x) f(x \land y ,y )$ for all $x,y \in P$. $P$ is distributive if and only if the strongly multiplicative invertible functions form a group.</p>
<p>My question is whether there is an easy way to obtain this group using Sage for a given $P$.</p>
https://ask.sagemath.org/question/53455/obtaining-a-group-from-distributive-lattices/?comment=53541#post-id-53541One can of course implement this group. It has a lot of elements, even if $K$ is finite, so the implementation depends on the needs. What should be done with this sage implementation? It is a good piece of work...Tue, 22 Sep 2020 12:29:10 +0200https://ask.sagemath.org/question/53455/obtaining-a-group-from-distributive-lattices/?comment=53541#post-id-53541