# problem1.txt
# Dan R. K. Ports <drkp@mit.edu>
# 6.170 PS2-1, 2004/02/12
# $Id: problem1.txt,v 1.1 2004/02/19 23:09:40 drkp Exp $

1. The one-line comments clarify the math being used by the
   computations that generate the return values of these functions.

2. A NaN is represented by a denominator of zero. RatNum.add and
   RatNum.mul generate new RatNums that have denominator 
   (this.denom * arg.denom), so if either number is NaN, then the
   denominator of the returned value will be zero, i.e. NaN. This is
   not true of a div call, so it is necessary to explicitly check
   whether the argument is NaN.

3. RatNum.parse is static because it generates a new object from only
   a string; it does not depend on the previous state of a RatNum
   object. This could also have been implemented as a constructor.

4. At the beginning of the constructor, the fields have not been
   initialized, so they should not be expected to satisfy the runtime
   invariant.

5. The two-argument constructor would be simpler: it wouldn't need to
   reduce the input.
   The checkRep method would be simplified to meet the weaker
   invariant.
   unparse() would be more complicated because it would need to
   reduce the number before outputting it.
   equals() and hashCode() would need to be made more complex: they
   would need to take into account that two rationals may be equal
   but in different unreduced forms.

6. The add/sub/mult/div calls need to return a new RatNum
   object. They are not allowed to modify the existing (immutable)
   object.