Assignment 5:   Worth 12% of the Homework grade


Due:  Monday, July 20th at 11:59 pm

To turnin program 5 (rat.py) from lectura, type
   % turnin 380assignment5 rat.py


1.  The object of this assignment is to become familiar with Python
    classes.

    You will be writing a class called Rational which implements 
    "infinite precision" rational numbers in Python.  For example:

     % python
     >> from rat import *
     >> a = Rational(3,4)     # 3 is the numerator, 4 is the denominator
     >> print a
     3/4
     >> b = Rational(4,4)
     >> print b               # Notice it prints in fully reduced form
     1/1
     >> c = a + b
     >> print c
     7/4                      # Your class supports addition 
     >> d = Rational(111111111111, 222222222222)
     >> print d
     1/1                      # Using infinite integers for both num and den

   Notice that the Rationals are always printed in fully reduced form.
   Internally, they should be represented that way as well.

   The class should support the standard operations: +,-,*,/

     >>> a = Rational(3,4)
     >>> b = Rational(3,4)
     >>> a + b
     rat.Rational(3,2)
     >>> print a + b
     3/2
     >>> print a - b
     0/1
     >>> print a * b
     9/16
     >>> print a/b
     1/1

   The class should also support <, <=, >, >=, ==, != and cmp
     >>> a = Rational(-1, 2)
     >>> b = Rational(1,2)
     >>> a < b
     True
     >>> a <= b
     True
     >>> a > b
     False
     >>> a >= b
     False
     >>> cmp(a,b)
     -1
     >>> a != b
     True
     >>> a is b
     False

   The class should return a "repr" string as many standard
   Python classes do: "rat.Rational(x,y)" (see examples below),
   where rat is the module, and Rational is the class in the
   module.  This is reminiscent of how they are constructed.

   If the denominator is ever 0, then the representation will
   always be 1/0 (our infinity).  Any mathematical operation (+,-,*,/)
   with 1/0 results in 1/0.  Two infinities are considered equal.
  
     >>> a = Rational(1,0)
     >>> b = Rational(2,3)
     >>> a+b
     rat.Rational(1,0)
     >>> a*b
     rat.Rational(1,0)
     >>> a/b
     rat.Rational(1,0)
     >>> a==b
     False
     >>> inf1 = Rational(1,0)
     >>> inf2 = Rational(2,0)
     >>> print inf1 == inf1
     True
     >>> inf1 < inf2
     False
     
   Be careful with the sign.  If a Rational is negative, it should always
   be associated with the numerator.

     >>> a = Rational(-1, -2)
     >>> print a
     1/2 
     >>> repr(a)
     'rat.Rational(1,2)'
     >>> b = Rational(3,-4)
     >>> print b
     -3/4
     >>> repr(b)
     'rat.Rational(-3,4)'
     >>> a + b
     rat.Rational(-1,4)
  
   Your class should work well with other basic types, namely
   longs, floats and ints.  In particular, you should support the
   following:

     >>> a = Rational(12)    # Construct, num implictly 1
     >>> print a
     12/1
     >>> b = Rational(1.5)   # Drop fractional part 
     >>> print b
     1/1
     >>> c = Rational(3.6)   # ...don't round, just drop
     >>> print c
     3/1
     >>> d = Rational(3,4)
     >>> print d
     3/4
     >>> d * 12              # In lhs*rhs, rhs can be float, int, long or 
     rat.Rational(9,1)       #  a Rational
     >>> 12 * d
     Traceback (most recent call last):
     File "<stdin>", line 1, in ?
     TypeError: unsupported operand type(s) for *: 'int' and 'Rational'

   So, your class should work well with longs, ints, floats and Rationals
   if a Rational is on the left hand side.    All +,-,*,/ should support
   ints, longs, floats, Rationals on the right hand side.   

     >>> a = Rational(1,2)
     >>> a + 2
     rat.Rational(5,2)
     >>> a - 1.0
     rat.Rational(-1,2)
     >>> a / 2L
     rat.Rational(1,4)
     >>> a * 17
     rat.Rational(17,2)

  Some other miscellany:  Your class should stay ints as long as possible,
  until it has to be a long.

     >>> import sys
     >>> a = Rational(sys.maxint)
     >>> print a
     9223372036854775807/1
     >>> repr(a)
     'rat.Rational(9223372036854775807,1)'
     >>> a  = a + 1
     >>> print a
     9223372036854775808/1
     >>> repr(a)
     'rat.Rational(9223372036854775808L,1)'

   As always, document your class well, using docstrings and make sure
   help works for your class.  We aren't requiring a particular format
   for help, but we are definitely going to be looking for one, as well
   as commenting and code style.