-- operator *
function mul( a, b )
  if ( ( a.type == "Transformation" ) and ( b.type == "Figure" ) ) then
    dxPushMatrix()
      a.func()
      b.func()
    dxPopMatrix()
  elseif ( ( a.type == "Transformation" ) and ( a.type == b.type ) ) then
    local tmp = function()
      a.func()
      b.func()
    end
    return new( tmp )
  else
  end
end
 
-- operator ^
function pow( a, n )
  if ( a.type == "Transformation" ) then
    local tmp = function() end
    local answer = new( tmp )
    while n > 0 do
      if ( n % 2 == 1 ) then
        answer = answer * a
      end
      a = a * a
      n = math.floor( n / 2 )
    end
    return answer
  else
  end
end
 
-- Figure class
function new( def_func )
  local obj = {}
  obj.type = "Figure"
  obj.func = def_func
  return obj
end
 
-- Transformation class
function new( def_func )
  local obj = {}
  obj.type = "Transformation"
  obj.func = def_func
  setmetatable( obj, { __mul = mul, __pow = pow } )
  return obj
end