From: Dan Connelly <lists@...>
Date: 2012-06-15T00:37:36+09:00
Subject: Re: sqrt of rational numbers

Looking at mathn.rb was instructive.

1. I forgot module_function -- this is needed when modifying Math 
functions to have "include Math" work correctly.
2. It uses "kind_of?" instead of "instance_of?".   This allows 
compatibility with sub-classes or Rational.  I suppose 
"x.responds_to?(:numerator) && x.responds_to?(:denominator)" would also 
have worked, but I'm not sure if I'm a huge fan of "duck typing", since 
it isn't obvious that every class which defines these functions is using 
them in a compatible fashion.  "kind_of?" is safer.
3. mathn solves the square root of integer problem ( sqrt(16) = 4, not 
sqrt(16) = 4.0), then redefines division of integers to produce a 
Rational (if not an exact integer), then simply uses square root on the 
numerator and denominator of the Rational.  So it's more comprehensive.

So the answer is: if you want these things to be well handled then use 
"mathn", albeit at the expense of speed.

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