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MathGroup Archive 2002

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Re: factoring quartic over radicals

  • To: mathgroup at smc.vnet.net
  • Subject: [mg37064] Re: factoring quartic over radicals
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Mon, 7 Oct 2002 05:26:31 -0400 (EDT)
  • Organization: Universitaet Leipzig
  • References: <anp0bs$qu0$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

In[]:=Factor[x^4 + x^3 + x^2 + x + 1, Extension -> {GoldenRatio,
1/GoldenRatio}]
Out[]=-((-3 - 2*x + Sqrt[5]*x + GoldenRatio*x - 3*x^2)*
   (3 + x + Sqrt[5]*x + GoldenRatio*x + 3*x^2))/9

Regards
  Jens

Steve Earth wrote:
> 
> Greetings MathGroup,
> 
> My name is Steve Earth, and I am a new subscriber to this list and also a
> new user of Mathematica; so please forgive this rather simple question...
> 
> I would like to enter the quartic x^4 + x^3 + x^2 + x + 1 into Mathematica
> and have it be able to tell me that it factors into
> 
> (x^2 + GoldenRatio x + 1) ( x^2 - 1/GoldenRatio x + 1)
> 
> What instructions do I need to execute to achieve this output?
> 
> -Steve Earth
> Harker School
> http://www.harker.org/


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