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MathGroup Archive 2002

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Re: factoring quartic over radicals

  • To: mathgroup at smc.vnet.net
  • Subject: [mg37029] Re: [mg37006] factoring quartic over radicals
  • From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
  • Date: Mon, 7 Oct 2002 05:23:52 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Since you already know the answer, the simplest way is:

In[51]:=
Factor[x^4 + x^3 + x^2 + x + 1, Extension -> {GoldenRatio}]

Out[51]=
(-(-1 - x + GoldenRatio*x - x^2))*(1 + GoldenRatio*x + x^2)

Andrzej Kozlowski

Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/


On Sunday, October 6, 2002, at 06:32 PM, 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/
>
>
>


On Sunday, October 6, 2002, at 06:32 PM, 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/
>
>
>
Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/



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