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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: [mg70439] Re: a fault in the Factor[] function for polynomials?
  • From: dimmechan at yahoo.com
  • Date: Mon, 16 Oct 2006 02:35:40 -0400 (EDT)
  • References: <egse02$cpp$1@smc.vnet.net>

No fault at all (I have converted everything to InputForm).

Options[Factor]
{Extension -> None, GaussianIntegers -> False, Modulus -> 0, Trig ->
False}

Information[Extension]

"Extension is an option for Factor, PolynomialGCD and related functions
which specifies what algebraic numbers to allow in the coefficients of
resulting polynomials."
Attributes[Extension] = {Protected}

ex = Expand[(x^4 + 2*Sqrt[3]*x^2 - 1)*(x^4 - 2*Sqrt[3]*x^2 - 1)]

1 - 14*x^4 + x^8

Factor[ex]

(1 - 4*x^2 + x^4)*(1 + 4*x^2 + x^4)

With the default setting Extension->None, Factor[poly] will treat
algebraic
number coefficients in poly like independent variables.

But

fex = Factor[ex, Extension -> Sqrt[3]]
(-2 + Sqrt[3] - x^2)*(2 + Sqrt[3] - x^2)*(-2 + Sqrt[3] + x^2)*(2 +
Sqrt[3] + x^2)

With a little effort you can return to ex

fex /. (a_)*(b_)*(c_)*(d_) :> Simplify[a*b]*Simplify[c*d]
(-1 - 2*Sqrt[3]*x^2 + x^4)*(-1 + 2*Sqrt[3]*x^2 + x^4)

Regards
Dimitris


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