Subject: Strange thing in Maxima: reduction of fraction
From: Leo
Date: Thu, 07 Dec 2006 17:33:45 +0000
On THU, 7 DEC 2006, Stavros Macrakis wrote:
> On 12/7/06, Leo <sdl.web at gmail.com> wrote:
>> On THU, 7 DEC 2006, Raymond Toy wrote:
>> But what about %o1 output? Isn't that a bug?
>
> Maxima's general simplifier does not simplify many cases. In
> particular, it does not perform GCD's of numerators and denominators
> -- it just looks for *surface* (syntactic) common factors, e.g.
> (a-1)/(a-1) => 1 but (a-1)/(1-a) => (a-1)/(1-a). To do fuller
> algebraic simplification, use ratsimp.
>
> As for why abs(p-q) simplifies to abs(q-p)... Maxima is trying to
> normalize the form of the argument to abs to allow certain
> simplifications to be easy, e.g. abs(p-q)/abs(q-p) => 1. This is at
> the cost of making other simplifications harder.
>
> Of course, this is not to say that Maxima's simplifier is the best
> possible simplifier. You might think, for example, that if it can
> simplify a/abs(a^2) => a, it could also simplify abs(a)/a^2 =>
> abs(1/a), but it (currently) can't at all (there is not even a
> special-purpose simplifier for this case). You can do this "by hand"
> by writing a simplification rule which rewrites abs(x) as signum(x)*x,
> but that's still not perfect... signum(a)/a - 1/(a*signum(a)) will not
> simplify to 0, even if you declare a to be nonzero.
>
> -s
Thank you for the explanation. That clears my confusion.
--
Leo