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MathGroup Archive 2006

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Re: a fault in the Factor[] function for polynomials?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg70447] Re: a fault in the Factor[] function for polynomials?
  • From: Peter Pein <petsie at dordos.net>
  • Date: Mon, 16 Oct 2006 02:36:18 -0400 (EDT)
  • References: <egse02$cpp$1@smc.vnet.net>

Roger Bagula schrieb:
> Expand[(x^4 + 2*Sqrt[3]x^2 - 1)(x^4 - 2*Sqrt[3]x^2 - 1)]
> 1 - 14x^4 + x^8
> Factor[%]
> (1 - 4x^2 + x^4)(1 + 4x^2 + x^4)
> 

Yes and there are many more "errors" in Factor:

try
Factor[%, Extension -> (Sqrt[3]{-1, 1})]
or
Factor[1 - 14*x^4 + x^8, Extension -> Sqrt[2 + Sqrt[3]*{-1, 1}]]
but the "worst" is definitely
Factor[1 - 14*x^4 + x^8,
   Extension -> Evaluate[x /. Solve[1 - 14*x^4 + x^8 == 0]]]

did you assume uniqueness of factorization into non-linear terms?

Peter


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