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MathGroup Archive 2002

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Re: Factorization

  • To: mathgroup at smc.vnet.net
  • Subject: [mg32209] Re: [mg32205] Factorization
  • From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
  • Date: Sun, 6 Jan 2002 03:38:24 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

One way:

In[1]:=
SolveAlways[{x^4 + 5*m^4 == (x^2 + a1*m^2 + b1*x*m)*
      (x^2 + a2*m^2 + b2*x*m), Modulus == 6}, {x, m},
   Mode -> Modular]

Out[1]=
{{a1 -> 1, a2 -> 5, b1 -> 0, b2 -> 0, Modulus -> 6},
   {a1 -> 5, a2 -> 1, b1 -> 0, b2 -> 0, Modulus -> 6}}


Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/

On Saturday, January 5, 2002, at 02:10  PM, Carlo Gabrieli wrote:

> Hi Mathgroup,
>
> I have to factor in (Z_6,+,x) the following bivariate polynomial
>
> x^4+[5]*m^4
>
> the result is (x^2+[5]*m^2)*(x^2+m^2), but how can I do this with
> Mathematica?
>
> Thanks in Advance
> Best Regards
> Carlo Gabrieli
> snail mail: Carlo Gabrieli
> Via San Giovanni d'Acri 15
> 30126 Lido di Venezia (VE)
> Tel.& FAX: 011-39-41-5264157
>
> e-mail: gabrieli at iuav.it
> gabrieli at flux.isdgm.ve.cnr.it
> gabrielic at libero.it
> gabrielic at inwind.it
>
> web pages: http://www.omitech.it/MERLIN/conn.htm
>
>
> =========================================================================
> =====
>
> "If you can't explain your research to your grandmother, then you
> don't understand it yourself"
>
> Richard Feynman
>
>
> "Update your bumper stickers, kids: Mac OS 8 = Windows 2010"
>
> David Pogue
>
> =========================================================================
> =====
>
>
>



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