[Edu-sig] Re: rationals

[Kirby Urner]

At 02:36 PM 10/10/2002 -0400, Guido van Rossum wrote:

>Except I don't like the 3r2 notation very much.  In my version it
>would become 3/2r, or 3r/2; parsed as 3 / 2r and 3r / 2, respectively.

Not clear if you mean 3r is by itself a rational (=3/1) as in:

   >>> a = 3r
   >>> a/2r
3/2

or would that be 3/2r ?

Entering 3r/2 on a command line looks to me like an invocation
of division between a rational (3r) and an integer (2), and so
would return 1.5 (float), i.e.

   >>> 3r/2
1.5


>And I'd also support 1.5r as a way to spell the same value.

Makes sense.

I get confused when I try to see / used both as an operator, and
as part of the name of a number.  Not sure if that's what you're
doing.

Would you go:

   >>> 1.5 .__rational__()
3/2r
   >>> 3/2r .__float__()
1.5

Perhaps you could do a short dialog in Python along the lines of:

    >>> a = 3r2
    >>> b = 1r2
    >>> a * b
3r4
    >>> float(a*b)
0.75
    >>> a + 2
5r2
    >>> a / 2
3r4

showing how it'd look in your implementation.

Note:  I'm deviating from the policy that rat / int --> float
in the last line.  Not sure if this is a good idea.  Maybe:

    int   / int   --> float     (float//float --> int)
    float / int   --> float     (int//int     --> int)
    rat   / int   --> rat   (?) (rat//rat     --> int)
    rat   / float --> float
    rat   / rat   --> rat

In other words, maybe it makes sense for / to coerce an int or
a long into a rat if the other arg is a rat.  This wouldn't
break code, as rat is a new type that couldn't get created by
old pre-rat code.

Coercion:

rat(3.1)    --> 31/10r   (?)
rat(2)      --> 2r
float(2/3r) --> 0.66666666666666663

rat() or rational()  ?


Kirby