function [Saver] = create_xi_cluster(X, Arg_Saver)
    % Date: 22.11.2010
    % Author: sz

    % TODO: the next function deletes multiple entries
    % in Saver and the entries of order 1
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    % Introduction
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    % interpret terms as points in lN^n space
    % x^3*y^2*z => (3,2,1) in lN^3

    % X is the set of all points, which we write like in
    % this example: (1,3) , (3,3), (1,2) are points of the set
    % Then X = [ 1,3 ; 3,3 ; 1,2 ]

    % Saver is global
    % global
    Saver_in = Arg_Saver;

    bigger2 = false;

    X2 = []; % initialize to prevent cases where X2 is empty
             % hence the program does not know where it came from
             % in these cases

% a fancy way to find out:
% does any point in X have a distance bigger than 2 to the (0,...0) ?
STX = sum(transpose(X));
        u = 1; % a counter (pretty technical stuff)
for i = 1:length(STX)
    if STX(i) > 2
        bigger2 = true; % bigger2 is dominant
        X2(u,:) = X(i,:) % create a new Matrix X2 (that way you filter
        u = u+1; % counter
        % out the others without having to delete it
        % [the ladder wouldnt work..]
    end
end


X = X2 % assign back

% if only one term is in X, you use the Halbieren-method
% FYI: if you dont consider this case you will get an
% error evaluating T = clusterdata(X,0.9), since that is only allowed
% for X with 2 elements or more...


if size(X,1) > 1


    % step 2 in the PDF
    % given the X, we create clusters
    T = clusterdata(X,2)

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    % if all "Clusters disjunct", that means, every cluster contains only 1 element
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    if max(T) == size(X,1)
      display('entering disjunct');
      M = []; % initialize

      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      % HALBIEREN - METHODE
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%

        % loop over Zeilen (Zeilenweise)
        for i = 1:size(X,1)

                display('check if only 1s and 0s');

                if sum(transpose(X(i,:))) <= size(X(i,:),2)

                % if there are only 1s and 0s in the X

                % new strategy, cut off only a vector of distance 1
                % in every process, namely the first 1 appearing

                for m = 1:size(X,2)
                    if X(1,m) == 1
                       X(1,m) = 0 ; % make it 0
                       break; % we only want to make one entry 0
                    end
                end


                else % check the Zeile for even / odd
                    display('entering even/odd');

                    even = false; % initialize it
                    % loop over Spalten
                    for j = 1:size(X,2)
                        if mod(X(i,j),2)== 0 % coord. is even
                            even = true;
                        end
                    end

                    if even % every coord. is even
                        M = [M; X(i,:)/2]; % add the half

                    else % there are uneven coordinates
                        % loop over Zeile
                        for e = 1:size(X,1)
                            % loop over Spalte
                            for f = 1:size(X,2)
                                if mod(X(e,f),2) == 1 % coord in (e,f) is odd
                                    Y(e,f) = X(e,f) - 1; % new Vector Y
                                end
                            end
                            M = [M; Y(e,:)];
                            % and add the difference
                            M = [M; X(e,:)-Y(e,:)];
                        end
                    end
                end
        end

      Saver = [Saver_in; M] % SAVE

      % now Recursion
      create_xi_cluster(M, Saver);

    %%%%%%%%%%%%%%%%%%%%%
    % not all disjunct and >= 2
    %%%%%%%%%%%%%%%%%%%%%
    elseif bigger2
    display('bigger2');

        % map the elements in X to cluster sets M(i) of number i
        % note to self: Faktorzerlegung von X zu Mengen M(i)

        number_of_clusters = max(T);

        for i = 1:length(T)
           Set.(['A',num2str(i)]) = []; % initializing
           for j = 1:length(T)
               if T(j)==i
                   Set.(['A',num2str(i)])=[Set.(['A',num2str(i)]); X(j,:)]
                   % set displayed as matrix (better to work with)
               end
           end
        end

        % now we have i sets Set.(['A',num2str(i)])

        % now, for every cluster, determine the "Stuetzstelle x_i*"
        % with the "method of the minimal projection" (see documentation PDF)

        % since Set.(['A',num2str(i)]) is a matrix, we can easily access
        % the entrys of Set.(['A',num2str(i)])


        % step 3
        % for all clusters Set.(['A',num2str(i)])
        for o = 1 : number_of_clusters
            % and for all number of columns of Set.Ao
            for p = 1:size(Set.(['A',num2str(o)]),2)
                x(o,p)=min(Set.(['A',num2str(o)])(:,p))  % x(o,:) is the "Stuetzpunkt" of Cluster o
            end
        end

        % step 4
        % for all t=length(Set.(['A',num2str(s)])) elements in Cluster Set.(['A',num2str(s)]),
        % calculate the differences

           b = 1;
        % for all clusters
        for a = 1:number_of_clusters

            for e = 1:size(Set.(['A',num2str(a)]),1)
               % the differences
               t(b,:)= Set.(['A',num2str(a)])(e,:) - x(a,:)
               b = b+1;
           end
        end

        % union the sets to one set (to one matrix M)
        display('union x and t to M');
        M = [x ; t]

        Saver = [Saver_in; M]

        create_xi_cluster(M, Saver);
    end

elseif isempty(X)
    display('done');

else %HALBIEREN DES EINZIGEN TERMS
        display('only 1 term');

        % sum of the only Zeile

        if sum(transpose(X)) <= size(X,2)
        % if there are only 1s and 0s in the X

            % new strategy, cut off only a vector of distance 1
            % in every process, namely the first 1 appearing

            for m = 1:size(X,2)
                if X(1,m) == 1
                   X(1,m) = 0 ; % make it 0
                   break; % we only want to make one entry 0
                end
            end

            M = X;

            Saver = [Saver_in; M] % SAVE
            create_xi_cluster(M, Saver); % Recursion

        else

            even = true; % initialize : uneven is dominant

            % loop over Spalten
            for j = 1:size(X,2)

                % there is only 1 Zeile, hence 1 in X(1,j)
                if mod(X(1,j),2)== 1 % coord. is uneven
                    even = false
                end
            end

            if even % every coord. is even
                M = X(1,:)/2; % add the half

            else % there are uneven coordinates
                % loop over Spalte
                for f = 1:size(X,2)
                    if mod(X(1,f),2) == 1 % coord in (e,f) is odd
                        Y(1,f) = X(1,f) - 1 % new Vector Y
                    else Y(1,f) = X(1,f); % else add the even coord.
                    end
                end
                M = [Y(1,:)]
                % and add the difference
                M = [M; X(1,:)-Y(1,:)]

            end

            Saver = [Saver_in; M] % SAVE

            create_xi_cluster(M, Saver); % Recursion

        end


end

end