Peter,

I hope this isn't considered too off-topic, but Mathematica has 4
distinct infinities.
The usual Infinity (+inf.0 in Scheme), -Infinity (-inf.0 in Scheme),
and the following:

- ComplexInfinity (might be represented in Scheme as (make-polar
+inf.0 +nan.0)), and
- DirectedInfinity[z] (might be represented in Scheme as (make-polar
+inf.0 (angle z))).

If we restrict our domain to inexact floating point real numbers,
these two infinities still represent something meaningful, and cannot
be converted to inexact rectangular complex numbers without losing
information. To make this less about polar complex numbers, consider
the logarithm of a directed infinity. (log (make-polar +inf.0 y))
should be +inf.0+yi, whatever y is. If y is an exact number, then
(imag-part (log ...)) should also be exact. I'm not sure how many
Scheme implementations actually store exact polar complex numbers this
way, but it helps keep numbers exact.

Regards,
Andrew Robbins

On Fri, Mar 23, 2012 at 3:13 PM, Peter Bex <Peter.Bex@xs4all.nl> wrote:
> Hi all,
>
> The report occasionally mentions "an inexact complex number" or
> "an exact complex number".  Does this imply that there's no such
> thing as a complex number of mixed exactness?
>
> Gambit, for example, allows this: 1/2+0.5i
> Other Schemes I've looked at (not that many, though) return a
> normalised complex number with both real and imaginary parts
> converted to inexact.
>
> As far as I can see, this only has impact on the behavior of
> eqv?, which needs to check that the exactness of both parts
> match and then compare both parts with the regular "=" procedure.
> I'm not sure about the usefulness of this (but I'm not convinced
> it's useless, either)
>
> Am I missing anything?
>
> Cheers,
> Peter
> --
> http://sjamaan.ath.cx
> --
> "The process of preparing programs for a digital computer
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