Re: factoring quartic over radicals
- To: mathgroup at smc.vnet.net
- Subject: [mg37034] Re: [mg37006] factoring quartic over radicals
- From: BobHanlon at aol.com
- Date: Mon, 7 Oct 2002 05:24:02 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
In a message dated 10/6/2002 6:31:10 AM, SteveE at harker.org writes:
>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?
>
soln = Factor[x^4 + x^3 + x^2 + x + 1,
Extension -> GoldenRatio] // Simplify
(x^2 - GoldenRatio*x + x + 1)*(x^2 + GoldenRatio*x + 1)
soln = Simplify /@
(soln /. -GoldenRatio -> -1 - 1/GoldenRatio)
(x^2 - x/GoldenRatio + 1)*(x^2 + GoldenRatio*x + 1)
soln // FunctionExpand // FullSimplify
x^4 + x^3 + x^2 + x + 1
Bob Hanlon