From: David Masover <ninja@...>
Date: 2009-11-20T15:11:34+09:00
Subject: Re: Exact (LISP-ish) calculations in Ruby?

On Thursday 19 November 2009 03:25:09 am Gavin Sinclair wrote:

> Furthermore, there's a Calculus-based algorithm (Newton's method, it's
> called in my syllabus, but I think it's properly called the Newton-
> Raphson method) for calculating square/cube/fourth/... roots to any
> desired accuracy.

Newton's Method, according to at least one Calculus textbook, is a way of 
finding roots (zeros) for any function for which you can calculate function 
values and derivatives. The example given is taking the cube root of seven, by 
rewriting the problem as:

x^3 - 7 = 0

The derivative of which is easy to calculate as 3x^2.

I wrote a program to do Newton's Method. It's one of the few times I wished I 
was using Lisp instead of Ruby, as I had no easy way of taking apart a block 
as source code to find its derivative. Instead, whenever I apply it, I have to 
take the derivative manually, or feed it through Maxima.

But I guess if what you wanted was something that knows how to do algebraic 
manipulation, without losing accuracy until you tell it to give you a float, 
there's always Maxima.