From: "Stephan Kämper" <Stephan.Kaemper@...>
Date: 2002-02-25T18:43:54+09:00
Subject: Re: inconsistence in class complex

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.

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.


> This wrongly comparision method leeds to the need of an additional
> equation operator ==, also something you would not expect. If you see

You need '==' to compare for equality, which is defined for complex numbers
(they'd be pretty much useless without it...).

> a=b you would expect the two numbers to be the same, not to have the
> same length.

Indeed after 'a=b' the numbers are the same, due to the assignment. ;-)


> Following the principle of least surprise I would strongly recommend
> for the next version of ruby to discard the complex operators <=> and
> ==, leaving only the operator = which should work as you would expect.

You might like to keep '<=>' - if keep in mind that this compares the
absolute vaues. That's OK.
As said above you like to have such a comparison - between _real_ numbers_
for work concerned with, eg., convergence of complex numbers

You definitely need '=' for complex assignment, as with more or less other
data type.
And you'll nedd '==' to compare two complex numbers for equality.

All three are correctly implemented in complex.rb, as far as I can tell.

The 'problem' is that '>' and the like ('>=' and friends) can be used with
complex numbers - although these operators are not defined with in class
Complex. I guess, and it's only a guess for now (!), that this is due to
some coercing happening when comparing complex numbers.

> 
> PS: Do not try to invent a comparision which is compatible with
> addition. This is possible but then the comparision will not be
> compatible with multiplication.

I second and repeat it (Sorry Dave & Andy for violating the DRYOU
principle):

Don't try to invent '<' and/or friends for complex numbers. It doesn't make
any sense.
Check your favourite complex analysis book for reference...


Happy rubying!

Stephan