Re: factoring quartic over radicals
- To: mathgroup at smc.vnet.net
- Subject: [mg37079] Re: [mg37006] factoring quartic over radicals
- From: "German BUITRAGO A." <gerbual at col2.telecom.com.co>
- Date: Tue, 8 Oct 2002 07:17:46 -0400 (EDT)
- References: <200210060932.FAA27437@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hello, Steve:
The key is in using the command Factor with the option Extension:
In[1]:=
Factor[x^4 + x^3 + x^2 + x + 1, Extension -> {GoldenRatio}]
Out[1]=
-((-1 - x + GoldenRatio*x - x^2)*(1 + GoldenRatio*x + x^2))
For manual verification you should keep in mind that:
1/GoldenRatio = GoldenRatio - 1
Best regards,
Germán Buitrago
----- Original Message -----
From: "Steve Earth" <SteveE at harker.org>
To: mathgroup at smc.vnet.net
Subject: [mg37079] [mg37006] factoring quartic over radicals
> 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/
>
- References:
- factoring quartic over radicals
- From: Steve Earth <SteveE@harker.org>
- factoring quartic over radicals