% the program gives the totally nondegenerate pg diagonals of length k of
% the interval square matrix [m,M]; precisely it gives a matrix U such that the
% first half and the second half of every row are the indices of a totally
% nondgenerate pg-diagonal of [m,M]


function U=nondegpgdiag(k,m,M)
  p=size(m,2);
X=zeros(1,0);
Y={};

%For every column we construct the array C given by the indices of the nondegenerate entries;
%we construct Y whose elements are the columns C so obtained;
%moreover we construct the row X with the indices of the columns with at least a nondegenerate entry 


  for j=1:p
	  C=zeros(0,1);
	  for i=1:p
		  if m(i,j)~=M(i,j)
		  C=[C;i];
		  end
		  end
		  if size(C,1)>0
		  X=[X,j];
Y(j)=C;
		  end
end

		  

		  
		  
		  U=zeros(0,2*k);
		    
A= nchoosek([1:size(X,2)],k);
		    for i=1:size(A,1)
			    R=sceltabis(Y(A(i,:)));
			    for j=1:size(R,1)
				    U=[U; [R(j,:), X(A(i,:))]];
				    end
				    end