function C = RomanNum
% C is a 3999-by-1 cell array where RN{k} is a string that specifies
% the Roman Numeral having value k.

  for a = 0:3
    for b = 0:9
      for c = 0:9
        for d = 0:9
          n = a*1000 + b*100 + c*10 + d;
          if n>0
             C{n} = [Thou2R(a) Hund2R(b) Tens2R(c) Ones2R(d)];        
          end
        end
      end
    end
  end
 
 function r = Ones2R(x)
 % x is an integer that satisfies 0<=x<=9
 % r is the roman numeral with value x
   Ones = {'I', 'II', 'III', 'IV', 'V', 'VI', 'VII', 'VIII', 'IX'};
   if x==0
      r = '';
   else
      r = Ones{x};
   end
   
 function r = Tens2R(x)
 % x is an integer that satisfies 0<=x<=9
 % r is the roman numeral with value 10*x
   Tens      = {'X', 'XX', 'XXX', 'XL', 'L', 'LX', 'LXX', 'LXXX', 'XC'};
   if x==0
      r = '';
   else
      r = Tens{x};
   end
   
 function r = Hund2R(x)
 % x is an integer that satisfies 0<=x<=9
 % r is the roman numeral with value 100*x
   Hundreds  = {'C', 'CC', 'CCC', 'CD', 'D', 'DC', 'DCC', 'DCCC', 'CM'};
   if x==0
      r = '';
   else
      r = Hundreds{x};
   end
   
 function r = Thou2R(x)
 % d is an integer that satisfies 0<=x<=3
 % r is the roman numeral with value 1000*x
   Thousands = {'M','MM','MMM'};
   if x==0
      r = '';
   else
      r = Thousands{x};
   end