From: jzakiya <jzakiya@...>
Date: 2009-12-30T09:45:06+09:00
Subject: Re: Roots Module


In looking for a nice home for my Roots module it seems
mathn.rb is a good fit because it adds the functions
sqrt|rsqrt to the Math module (do sqrt x, not x.sqrt).
So I copied my roots.rb file into the same dir under lib
which has mathn.rb, and add the follow code to mathn.rb
at the top, under it's 'require' list: [Ruby 1.9.1p243]

require 'roots'

class Integer; include Roots end
class Float;   include Roots end
class Rational
  include Roots
  def self.root(x);  self.to_f.root  end
  def self.roots(x); self.to_f.roots end
end

I had to do Rational like this because
Rational(x/y).root(n) produced a NoMethodError, but
Rational.to_f.root(n) takes care of that. I would like
Complex(x,y).root(n) too, but I haven't figured out a
nice way to do that yet, to match:  sqrt Complex(x,y)
though you can do: Complex(x,y)**n**-1  for all roots.
It would be nice to have the simpler syntax, though.

So now in irb if you load this in:

>require 'mathn'
>include Math   # to also get functions sqrt|rsqrt

So
>sqrt -9   => (0+3i)
>-9.root 2 => (0.0+3.0i)

and
>sqrt Rational(25/81)   => (5/9)
>Rational(25/81)**(1/2) => (5/9)
>Rational(25/81)**2**-1 => (5/9)
>Rational(25/81).root 2 => (5/9)  # but
>Rational(25/81)**0.5   => 0.55555555555556

along with Rational(x/y).roots(n,opt)

Everything seems to work with only one known QUIRK.

mathn.rb adds this to classes Fixnum and Bignum:

class Fixnum|Bignum
  remove_method :/
  alias / quo

  alias power! ** unless defined?(0.power!)

  def ** (other)
    if self < 0 && other.round != other
      Complex(self, 0.0) ** other
    else
      power!(other)
    end
  end
end

The line:  alias power! ** unless defined?(0.power!)

causes an error for Bignums, I get for (X).root(n) a
NoMethodError: undefined method `power!' for (X):Bignum
but not when I do a Fixnum (x).root(n).

I can do (X).0.root[s](n) to get around this problem,
and redefine these methods in Bignum like for Rationals,
but that's a hack for a seemingly simple resolution.

When I comment out the: # unless defined?(0.power!)
in class Bignum the problem goes away.

Also, if I don't load mathn.rb, and just load roots.rb
and then mixin Roots in Integer and Float, as I did
originally, I can do Bignums with no problems.

Any ideas on what's the problem with Bignum class here?

Thus, by doing this in mathn.rb, you get all the roots
of real and rational numbers, and not just the sqrts.