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MathGroup Archive 2006

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Re: Cannot solve 3x3 Eigensystem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68630] Re: Cannot solve 3x3 Eigensystem
  • From: dimmechan at yahoo.com
  • Date: Sun, 13 Aug 2006 05:52:52 -0400 (EDT)
  • References: <ebhi7q$12a$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi, kdittmer

I can't understand what tou mean by "exact" solution.
Your solution containing Root objects is exact.
Anyway, you can use the Built in function ToRadicals.

$Version
 5.1 for Microsoft Windows (October 25, 2004)

??ToRadicals
ToRadicals[expr] attempts to express all Root objects in expr in terms
of radicals.More...
Attributes[ToRadicals]={Protected}
Options[ToRadicals]={Cubicsï?®True,Quarticsï?®True}

However, what you get is a huge expression that I donâ??t know if it
useful for you.

BTW, while version 5.1 needs 0.375 sec. in my system to execute the
command

 FullSimplify[Eigensystem[{{a1, b1, 0}, {b1, a2, b2}, {0, b2, a3}},
Cubics-> True], {b1, b2, a1, a2, a3} ï?? Reals]

in version 5.2, I could not obtain the result of above command after 3
minutes so I give up.
I guess something here.
Any ideas?


kdittmer wrote:
> The result of
>
> FullSimplify[Eigensystem[{{a1, b1, 0}, {b1, a2, b2}, {0, b2, a3}},
> Cubics-> True], {b1, b2, a1, a2, a3} \[Element] Reals]
>
> is unfortunately containing Root[].
> 
> How do i get my exact solution?


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