[GAP Forum] Atoms of a boolean algebra of sets

[Johannes Hahn]

Dear forum,

 

Let’s say a have a list of subsets of a fixed finite set $\Omega$. Is there a nice and easy way to find the atoms of the Boolean algebra generated by these sets? Of course, I could implement this by hand, but it seems to me that something like this probably already exists and I simply had bad luck finding it.

 

A related question: Let’s say I have a list of partitions of $\Omega$ (i.e. a set of pairwise disjoint subsets that cover all of $\Omega$). Is there a nice and easy way to find the common refinement of all these partitions?

 

Best wishes

Johannes Hahn.