5. 2. 2 Addition

The addition of the maps can be implemented for the affine expression as follows:

 self operator+=(self& s)
 {
   map_iter_t iter = coefficients.begin();

   while (iter != coefficients.end())
    s.coefficients[(*iter).first] += (*iter).second;
 
    s.right_hand_side += right_hand_side;
 }

Other operations such as subtraction or multiplication can be implemented in the same manner.