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MathGroup Archive 2002

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Re: No Subject

  • To: mathgroup at smc.vnet.net
  • Subject: [mg32304] Re: No Subject
  • From: BobHanlon at aol.com
  • Date: Sat, 12 Jan 2002 05:18:15 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 1/11/02 6:12:41 AM, Matthias.Bode at oppenheim.de writes:

>Factor[a^2 - b^2] yields - predictably -
>
>(a - b)*(a + b).
>
>The question "what yields the factorization of a^2 + b^2" is not
>far-fetched.
>
>How can I coax MATHEMATICA into giving: (a - I*b)*(a + I*b)?
>Are there more "simple" solutions of the same structure (... - ...)*(...
>+
>...) or some wizardry like (... + or - ...)^t, where t is some composite
>expression ?
>

Factor[Table[a^(2n)+b^(2n), {n, 3}],
 GaussianIntegers -> True]

{(a - I*b)*(a + I*b), (a^2 - I*b^2)*(a^2 + I*b^2),
 
  (a - I*b)*(a + I*b)*(a^2 - I*b*a - b^2)*
   (a^2 + I*b*a - b^2)}


Bob Hanlon
Chantilly, VA  USA


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