From: GOTO Kentaro <gotoken@...>
Date: 2002-02-25T20:07:59+09:00
Subject: Re: inconsistence in class complex

In message "Re: inconsistence in class complex"
    on Mon, 25 Feb 2002 18:43:54 +0900,
    Stephan K�mper <Stephan.Kaemper@Schleswig-Holstein.de> writes:

> Juergen Katins wrote:
> > 
> > While translating the book "Programming Ruby" by Dave Thomas and
> > Andrew Hunt into german language (see
> > http://home.vr-web.de/juergen.katins/ruby/) I stumbled arcoss an
> > irritating inconsistence in the standard library. In the class complex
> > there is a comparision operator <=>.
> > 
> > <=> ref <=> other -> -1, 0, +1
> > Returns ref.abs <=> other.abs.
> > 
> > In mathematical meanings this makes no sense! You can not compare
> > complex numbers! 
> 
> That depends: Comparing to complex numbers 'by absolute value' make perfect
> sense, eg. when dealing with sequences of convergent complex numbers.
> Anyway, talking 'mathematicese' you'd likely define a metric upon which to
> construct a definition for lenght (or absolute value).
> 
> Notwithstanding, comparing complex numbers, as with '<' or '>', makes no
> sense indeed.
> 
> Now, while I think that the current behaviour of <=> can be accepted, '>'
> and '<' shouldn't work as currently implemented.

Here is another odd: 

             -2 == Complex(-2,0)  #=> true
              1 == Complex(1,0)   #=> true
            -2  <=> 1             #=> -1
  Complex(-2,0) <=> Complex(1,0)  #=> 1

This says (a == b) && (c == d) but (a <=> c) != (b <=> d). 
 
> As far as I see, Complex inherits from Numeric and that's OK.
> And it doesn't include Comparable, which relects the fact that complex
> numbers can'T be compared with '>' and the like.

I agree halfly.  

In Ruby world, Module forms partialy order, i.e., A < B and B < C
implies A < C for any module A,B,C.  Now, we have Complex < Numeric
and Numeric < Comparable, therefore Complex < Comparable automatically
even if Complex#<=> would be undefined. 

There are other Ruby-definable strange numeric sets, e.g., Hamilton's
Quotanion, which has four imaginary units.  So, Complex isn't only
special.

However, undef Complex#<=> and ignoring the fact Complex < Comparable
seems a practical and acceptable option, IMHO.  To go rigorous,
Numeric must not include Comparable but Integer, Float and Rational
must include severally. 

-- Gotoken