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MathGroup Archive 2004

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Re: Equation - problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48993] Re: [mg48981] Equation - problem
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sat, 26 Jun 2004 01:55:37 -0400 (EDT)
  • References: <200406252152.RAA21757@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On 26 Jun 2004, at 06:52, RAFAL wrote:

> Hi
>
> I need a good package for computing the equation like below:
>
> Reduce[r^2*(x^q - 1)*(( - r*x*(x^q - 1 ))^q - 1) == 1 && r >= 0 &&
> 0 <= x <= 1 && q > 0, x, Reals]
>
> Thanks
>
> rak
>
If you mean that you want to compute x as an explicit function of r and 
q, than not only does no software for this exists know, but almost 
certainly will never exist in the future either.

If, on the other hand, all you want is to find a triple of reals x,q,r 
that approximately satisfy the equation than Mathematica can do it 
quite easily:


Chop[NMinimize[
    {Abs[r^2*(x^q - 1)*(((-r)*x*(x^q - 1))^q - 1) - 1],
     0 <= r <= 10 && 0 <= x <= 1 && 0 <= q <= 10},
    {x, r, q}]]

{0, {q -> 0.3562694885703915, r -> 7.731875654183964,
    x -> 0.6779077010660948}}


Andrzej Kozlowski
Chiba, Japan
http://www.mimuw.edu.pl/~akoz/


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