Dear Johannes,
As to your second question: I think it should be straightforward to adapt
RCWA's internal function
'CommonRefinementOfPartitionsOfZ_NC' for this purpose. That function computes
the common refinement of a set of partitions of the integers into finitely many
residue classes:
#############################################################################
##
#F CommonRefinementOfPartitionsOfZ_NC( <partitions> ) . . special case R = Z
##
InstallGlobalFunction( CommonRefinementOfPartitionsOfZ_NC,
function ( partitions )
local table, partition, mods, res, m,
pow, mj, r, i, j, k;
mods := List(partitions,P->List(P,Mod));
res := List(partitions,P->List(P,Residues));
m := Lcm(Concatenation(mods));
table := List([1..m],i->0);
pow := 1;
for i in [1..Length(partitions)] do
for j in [1..Length(partitions[i])] do
mj := mods[i][j];
for r in res[i][j] do
for k in [r,r+mj..r+(Int(m/mj)-1)*mj] do
table[k+1] := table[k+1] + pow;
od;
od;
pow := pow + pow;
od;
od;
partition := EquivalenceClasses([1..m],r->table[r]);
return Set(List(partition,r->ResidueClassUnion(Integers,m,r-1)));
end );
Hope this helps,
Stefan
________________________________
From: Johannes Hahn <johannes.h...@uni-jena.de>
Sent: Tuesday, February 26, 2019 12:01:15 AM
To: forum@gap-system.org
Subject: [GAP Forum] Atoms of a boolean algebra of sets
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.
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