From: oinkoink+unet@... (Bret Jolly)
Date: 2003-05-04T03:52:09+09:00
Subject: Re: MathN

Dave Thomas <dave@pragprog.com> wrote in message news:<3EA7FF8F.3080500@pragprog.com>...
> I'm trying to get to grips with the 'mathn' library. I can see what it 
> _does_, but I'm trying to see why it does it. Is it emulating a mathn 
> library in some other language, or is it simply there to make arithmetic 
> more accurate?

  Let me try again, since the usenet gremlins seem to have intercepted
my earlier post (although Jim Freeze saw it somehow).

   The easiest way to see the importance of 
the mathn library is to consider what happens
if you try to use Rational, Complex, or Matrix,
without requiring mathn.  (The mathn library
requires rational.rb, complex.rb, and matrix.rb.
and then makes them "play nice" with one another.)

   First look at complex numbers without mathn.
irb(main):001:0> require 'complex'
true
irb(main):002:0> minus_two = Complex(-2, 0)
Complex(-2, 0)
irb(main):003:0> minus_two < 1
false   # fubar!
irb(main):004:0> minus_two > 1
true    # fubar!


irb(main):001:0> require 'mathn'
true
irb(main):002:0> minus_two = Complex(-2, 0)
-2
irb(main):003:0> minus_two < 1
true    # correct
irb(main):004:0> minus_two > 1
false   # correct


  Now try matrix.rb
irb(main):001:0> require 'matrix'
true
irb(main):002:0> m = Matrix[[2, 7], [3, 4]]
Matrix[[2, 7], [3, 4]]
irb(main):003:0> m.det
-6      # fubar!
irb(main):004:0> m.inv
Matrix[[-1, 1], [0, -1]]  # fubar!

irb(main):001:0> require 'mathn'
true
irb(main):002:0> m = Matrix[[2, 7], [3, 4]]
Matrix[[2, 7], [3, 4]]
irb(main):003:0> m.det
-13     # correct             
irb(main):004:0> m.inv
Matrix[[-4/13, 7/13], [3/13, -2/13]] # correct

   Now try rational.rb
irb(main):001:0> require 'rational'
true
irb(main):002:0> two = Rational(2, 1)
Rational(2, 1)
irb(main):003:0> 2 == two
true   # Gratifying, but...
irb(main):004:0> two/3
Rational(2, 3)
irb(main):005:0> 2/3
0  # inappropriate when Rational is available.
   # equal numbers should act equal!

irb(main):001:0> require 'mathn'
true
irb(main):002:0> two = Rational(2, 1)
2
irb(main):003:0> two/3
2/3
irb(main):004:0> 2/3
2/3  # integers and rationals now play nice

   In conclusion, if you want to use the built-in
libraries rational, complex, and matrix, you
should require mathn.

                  Regards, Bret