From: Colin Bartlett <colinb2r@...>
Date: 2009-12-20T23:51:10+09:00
Subject: Re: Correcting complex math

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.