From: Robert Klemme <shortcutter@...>
Date: 2011-04-07T22:43:52+09:00
Subject: Re: Hash Surprises with Fixnum, #hash, and #eql?

On Thu, Apr 7, 2011 at 3:21 PM, Phillip Gawlowski
<cmdjackryan@googlemail.com> wrote:
> On Thu, Apr 7, 2011 at 1:53 PM, Robert Klemme
> <shortcutter@googlemail.com> wrote:
>>
>> Actually it's Numeric which is correct because not every Complex _is a_ Float!
>
> Unless you convert from polar form* to Cartesian form:
>
> Let's take "45e^(j * 44°)":
>
> 32.37029101523930127102246035055203587038080515238845970760... +
> 31.25962667065487789953828347402088034639160866937838052053... i
>
> From <http://www.wolframalpha.com/input/?i=45*e^%2844%C2%B0i%29>.
>
> * Which you are much more likely to encounter than the Cartesian form,
> considering complex numbers are most useful when dealing with wave
> forms.

My math is a bit rusty in that area, but I don't think your argument
holds: cartesian and polar are just two ways to represent a complex
number.  But this does not change numeric properties of the class of
complex numbers.  No matter what representation you use, (0+1i) is
neither a real number (what float conceptually models) nor a rational
number (what float technically implements).  Instead, real and
rational numbers are both subsets of complex.

If you see inheritance as "is a" relationship then inheritance would
be Rational < Real < Complex but not the other way round.  Otherwise
you cannot use a subclass instance everywhere you were using a
superclass instance.

Further links:

http://en.wikipedia.org/wiki/Rational_number
http://en.wikipedia.org/wiki/Real_number
http://en.wikipedia.org/wiki/Complex_number

Kind regards

robert

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