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