A good python Rational class

Python implements integers, floats, decimals and complex numbers. But no rationals. PEP 239, "Adding a Rational Type to Python", suggests ... the addition of a rational type to python. But alas. Guido said no. And that was 2001.

So developers everywhere implement their own. Duration math depends crucially on rational arithmetic and so Víctor and I are no exception. My first implementation was in 2005, I think Víctor followed soon after, and we've shared a relatively robust implementation this year. And, just this week, we've reimplemented yet again.

Some features.

The initializer requires numerator but leaves denominator optional.

   >>> p = Rational(13, 8)
   >>> p
   13/8

   >>> q = Rational(2)
   >>> q
   2

Unary negation, inversion and absolute value work the way you think they do.

   >>> -p
   -13/8

   >>> ~p
   8/13

   >>> abs(p)
   13/8

So do the inequalities.

   >>> p < q, p <= q, p == q, p >= q, p > q
   (True, True, False, False, False)

Integers work too.

   >>> p
   13/8

   >>> p < 2, p <= 2, p == 2, p > 2, p >= 2
   (True, True, False, False, False)

Arithmetic __add__, __sub__, __mul__, __div__ and even __truediv__ all work.

   >>> p, q
   (13/8, 2)

   >>> p + q
   29/8

   >>> p - q
   -3/8

   >>> p * q
   13/4

   >>> p / q
   13/16

Things that are supposed to be commutative are. Others aren't.

   >>> p + q == q + p, p * q == q * p
   (True, True)

   >>> p - q == q - p, p / q == q / p
   (False, False)

Right-operators __radd__, __rsub__, __rmul__, __rdiv__ and __rtruediv__ make integers work here too.

   >>> p
   13/8

   >>> 2 + p  
   29/8

   >>> 2 - p
   -3/8

   >>> 2 * p
   13/4

   >>> 2 / p
   16/13

Floor division comes up every once in a while.

   >>> Rational(93, 8) // 2
   5

And you can compose with rational mod.

   >>> Rational(93, 8) % 2
   13/8

   >>> Rational(93, 8) % Rational(2, 3)
   7/24

   >>> 93 % Rational(2, 3)
   1/3

Coercion works for int and float

   >>> p
   13/8

   >>> int(p)
   1

   >>> float(p)
   1.625

And there're set and copy methods.

   >>> p.set(15, 16)
   >>> p
   15/16

   >>> p.copy( )
   15/16
   >>> id(p) == id(_)
   False

The code is here. If you like -- or find bugs -- let us know.