Re: Re: Big problem in solving radicals.
- To: mathgroup at smc.vnet.net
- Subject: [mg41944] Re: [mg41916] Re: Big problem in solving radicals.
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Wed, 11 Jun 2003 03:49:34 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
One problem that you have to keep in mind is that
CylindricalAlgebraicDecomposition, which is based on a beautiful
algorithms (due to Collins) in real algebraic geometry works for
polynomial equations (or equations that can be converted to polynomial
equations). The fact that it works in your original case (as noticed by
Paul Abbott) at all is a kind of "extra feature". In fact if you enter
a more complex equation with radicals you will get the message:
".....is not a logical formula consisting of polynomial equations and
inequalities
in {x,a} with rational number coefficients."
Secondly, the running time of CylindricalAlgebraicDecomposition is
double exponential in the number of free variables. The number of
"cells" produced by the algorithm is also double exponential. So if
your problem is of the kind I suspect it is, you will have to wait a
pretty long time.
Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/
On Tuesday, June 10, 2003, at 05:46 pm, Davide Del Vento wrote:
> Although "CylindricalAlgebraicDecomposition" works well also with many
> variables (e.g. try with a/(b+sqrt(c/x)) == F), it seems to block for
> my original problem, but I'm working with it. Keep in mind that
> "CylindricalAlgebraicDecomposition" is much more than what I need,
> that is a solution as can be simply obtained by Solve and the range of
> parameters where it is valid (see my answer to Andrzej Kozlowski too)
>
>