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

• To: mathgroup at smc.vnet.net
• Subject: [mg70436] Re: [mg70395] a fault in the Factor[] function for polynomials?
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Mon, 16 Oct 2006 02:35:21 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200610150419.AAA12686@smc.vnet.net>
• Reply-to: murray at math.umass.edu

Why do you think this is a "fault" in Factor??

   Simplify[(1 - 4x^2 + x^4)(1 + 4x^2 + x^4) == (x^4 + 2*Sqrt[3]x^2 - 1)(
           x^4 - 2*Sqrt[3]x^2 - 1)]
True

You can even factor additional ways, e.g.:

   Factor[1 - 14x^4 + x^8, Extension->Sqrt[3]]
(-2 + Sqrt[3] - x^2)*(2 + Sqrt[3] - x^2)*
  (-2 + Sqrt[3] + x^2)*(2 + Sqrt[3] + x^2)

Roger Bagula wrote:
> 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)
> 
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

• References:
  • a fault in the Factor[] function for polynomials?
    • From: Roger Bagula <rlbagula@sbcglobal.net>