From: Paul Smith <paul@...>
Date: 2009-12-21T00:03:06+09:00
Subject: Re: Correcting complex math

On Sun, Dec 20, 2009 at 2:51 PM, Colin Bartlett <colinb2r@googlemail.com> wrote:
> If this can be made to work, it might be useful.
> Two thoughts that occur to me are:
>
> 1. The code you show would probably need to use Rational(?),
>   otherwise 1/n (or 1.0/n) may not be what one thinks it is.
>
> 2. What would one do with a number (Float or Rational)
>   which is arbitrarily close to 1/n but which is not 1/n?
>
> I'd also like to take the opportunity of this thread
> to suggest removing (!) something from Complex,
> unless anyone can make a good case for retaining it:
>
> require "complex"
> n = -2                #=> -2
> p = 1                 #=> 1
> cn = Complex( n, 0 )  #=> Complex(-2, 0)
> cp = Complex( p, 0 )  #=> Complex(1, 0)
> n > p                 #=> false
> cn > p                #=> true
> cn > cp               #=> true
>
> The Complex numbers are not an "ordered field",
> at least not in any normally useful sense.
>
> At the moment if either x or y is Complex
> then  x <=> y  is calculated as  x.abs <=> y.abs;
>
> # File complex.rb, line 312
>  def <=> (other)
>    self.abs <=> other.abs
>  end
>
> I think that can be misleading (see the examples above),
> and I would prefer it if "<=>" and "<", etc,
> were *not* defined for Complex,
> and if one wants to compare absolute values
> then one should do so explicitly.
>
>

If you're messing around with complex variables and you come across
the '>' operator, what else would you expect it to do other than
compare absolute values?  There's no room for confusion here, it's
just a syntax shortcut like we have in so many other places in Ruby.

-- 
Paul Smith
http://www.nomadicfun.co.uk

paul@pollyandpaul.co.uk