function res = BetheBCS(x,g)
%Defines function to be solved to obtain rapidities for the BCS model
%set spin to 1/2 and asume equidistant spacing of energies: e_i =i
%In this example, L=16, M=8

%Explizit komplexe Rechnung erzwingen
v = x(1,:) + i*x(2,:);

% Anzahl Spin Paare nach oben
M = 8;
% Anzahl Paare
L = 16;

e = 1:L; % Energien epsilon
s = ones(L,1)*0.5; % s = 0.5 (Spin)

F = NaN(M,1);

%Initialisierung der Funktion
for row = 1 : M
    
   sum2 = 0;
   for k = 1 : L
       sum2 = sum2 + s(k)/(v(row) - e(k));
   end
   
   sum3 = 0;
   for j = 1:M
      if ( j ~= row)
          sum3 = sum3 + 2/(v(row)-v(j));
      end
   end
  term1 = 1/(g);
  
  F(row)=term1+sum2-sum3;
          
end


res = [real(F)';imag(F)'];

end