function EC = hequiv_classes(S)
% for all a,b in S, a H b   iff a R b and  a L b
% brute force

[n,n] = size(S);
EQ = zeros(n);
for i=1:n
  for j=i+1:n
    Sil = Sa(S,i);
    Sjl = Sa(S,j);
    Sir = aS(S,i);
    Sjr = aS(S,j);
    EQ(i,j) = (seteq(Sil,Sjl) & seteq(Sir,Sjr)) ;
  end
end

EQ = EQ+EQ'+eye(n);
X = 1:n;
EC={};
while ~isempty(X)
    x = X(1);
    Ex = find(EQ(x,:));
    EC{end+1} = Ex;
    X = setdiff(X,Ex);
end
return


function Si = Sa(S,a)
[n,n] = size(S);
Si = [];
for i=1:n
  Si(end+1) = S(i,a);
end
return

function Si = aS(S,a)
[n,n] = size(S);
Si = [];
for i=1:n
  Si(end+1) = S(a,i);
end
return