function [R,L,J,H] = get_rljh(S)
% computes the equivalence relations of Green: R, L, J and H


[n,n] = size(S);
R = zeros(n,n);
L = zeros(n,n);
J = zeros(n,n);
H = zeros(n,n);
I = eye(n);


for i=1:n
  for j=i+1:n
    Tr1 = aS(S,i);
    Tr2 = aS(S,j);
    R(i,j) = seteq(Tr1,Tr2);
    Tl1 = Sa(S,i);
    Tl2 = Sa(S,j);
    L(i,j) = seteq(Tl1,Tl2);
    Tj1 = SaS(S,i);
    Tj2 = SaS(S,j);
    J(i,j) = seteq(Tj1,Tj2);
    H(i,j) = R(i,j) * L(i,j);
  end
end
R = R+R'+I;
L = L+L'+I;
J = J+J'+I;
H = H+H'+I;
return




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

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

function T = SaS(S,a)
[n,n] = size(S);
T = [];
for i=1:n
  for j=1:n
    T(end+1) = S(S(i,a),j);
  end
end
T = unique(T);
return