[Python-Dev] PEP239 (Rational Numbers) Reference Implementation and new issues

Andrew Koenig ark at research.att.com
Thu Oct 3 03:10:52 CEST 2002

Guido> [Andrew Koenig]
>> Much as I like APL, I'd rather use Scheme's numeric model.

Guido> I've heard that before, but I've also heard criticism of
Guido> Scheme's numeric model.  "It works in Scheme" doesn't give me
Guido> the warm fuzzy feeling that it's been tried in real life.

...and "It works in APL" does?

More seriously, there aren't that many languages with
infinite-precision rationals, which means there aren't
all that many precedents.

I find the partial ordering among Python's types interesting.
If we use "<" to mean "is a strict subset of", then

   int < long < rational  (except perhaps on machines with 64-bit int,
			   which opens a different can of worms entirely)

   int < float < rational

   float < complex

Excluding complex, then, adding rational to the numeric types makes
the numeric types a lattice.  We could make all of the numeric types
a lattice by adding a "complex rational" type:

                  complex rational
                        |      \___
                        |          \
                     rational    complex
                      /    \   ____/
                     /      \ /
                  long     float
                    \     __/
                     \   /     
                      \ /

What's nice about a lattice is that for any two types T1 and T2, there
is a unique minimum type T of which T1 and T2 are both subsets (not
necessarily proper subsets, because T1 could be a subset of T2 or vice

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