Re: square root denominators

From: Oscar Lanzi III (ol3_at_webtv.net)
Date: 02/25/05 

Date: Thu, 24 Feb 2005 21:32:14 -0600

In some applications it is actually more profitable to rationalize the
NUMERATOR. Generally this involves variable expressions as opposed to
numbers. In another thread I describe a situation where I had to solve
by computer a quadratic equation of the form a^2 + bx + c = 0 with a
being potentially zero. Using a rationalized-numerator version of the
formula, c/(-b (+/-) sqrt(b^2-4ac)), allows one to avoid a zero or
near-zero denominator in such a case. Another example is integrating
sqrt((1+x)/(1-x)) dx by first rendering the integrand as
(1+x)/sqrt(1-x^2).

--OL

Relevant Pages

  • Re: rational arithmetic library?
    ... I made a mistake: Bigloo does not support rationals: ... Unbound variable -- rationalize ... Unbound variable -- numerator ... Unbound variable -- denominator ...
    (comp.lang.lisp)
  • Re: calculus-derivatives
    ... Rationalize the numerator: ... Substitute t for h by the equation h = x/t ...
    (sci.math)