RE: factoring quartic over radicals
- To: mathgroup at smc.vnet.net
- Subject: [mg37048] RE: [mg37006] factoring quartic over radicals
- From: "DrBob" <drbob at bigfoot.com>
- Date: Mon, 7 Oct 2002 05:25:03 -0400 (EDT)
- Reply-to: <drbob at bigfoot.com>
- Sender: owner-wri-mathgroup at wolfram.com
It's a little ugly, but here's my solution:
x^4 + x^3 + x^2 + x + 1
Simplify@Factor[%, Extension -> {GoldenRatio, 1/GoldenRatio}]
Collect[%[[2]]/3, x]Collect[%[[3]]/3, x]
% /. Sqrt[5] -> 2GoldenRatio - 1
% // Simplify
Collect[#, x] & /@ %
% /. {1 - GoldenRatio -> -1/GoldenRatio}
FullSimplify@Expand@%
(The last line is a check.)
Bobby
-----Original Message-----
From: Steve Earth [mailto:SteveE at harker.org]
To: mathgroup at smc.vnet.net
Subject: [mg37048] [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/