Re: solve equation and domains
- To: mathgroup at smc.vnet.net
- Subject: [mg42127] Re: [mg42103] solve equation and domains
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Fri, 20 Jun 2003 04:57:27 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Yes and No. In principle
Experimental`CylindricalAlgebraicDecomposition[{x^3 + (s + b + 1)*x^2 +
(r + \
s)*b*x + 2*b*s*(r - 1) == 0, r > 1}, {s, b, r, x}]
should do it, but you have too many variables to expect an answer in a
reasonable time. If however you reduce the number of variables by
substituting a value for s, for example 1, then you can get the answer
pretty quickly:
With[{s =
1}, Experimental`CylindricalAlgebraicDecomposition[{x^3 + (s + b +
1)*x^2 +
(r + s)*b*x + 2*b*s*(r - 1) == 0, r > 1}, {r, b, x}]]
or, if you prefer
With[{s =
1}, Experimental`CylindricalAlgebraicDecomposition[{x^3 + (s + b +
1)*x^2 +
(r + s)*b*x + 2*b*s*(r - 1) == 0, r > b}, {r, b, x}]]
You can of course try running your original case (with 4 variables) and
waiting, but since the algorithm has a double exponential running time
(in the number of free variables) you are probably out of luck. (If you
ever arrived at an answer it would be dreadfully complicated).
This, by the way, is not Mathematica's fault: the algorithm that you
need to use to solve this kind of problem has very bad complexity with
respect to the number of variables, so what you probably need is a
stroke of genius rather than a fast computer.
Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/
On Thursday, June 19, 2003, at 04:59 PM, anto wrote:
> I must solve this equation x^3+(s+b+1)*x^2+(r+s)*b*x+2*b*s*(r-1)=0
> I wish the solutions in the domain r>1.
> It 's possibile to do on mathematica?
> If i can it's ,possible to solve in the domain r>b?
>
> Thx
>
>
>