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MathGroup Archive 2001

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Re: Factor[1+x^4]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg26870] Re: [mg26855] Factor[1+x^4]
  • From: BobHanlon at aol.com
  • Date: Fri, 26 Jan 2001 01:27:19 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

?Factor

"Factor[poly] factors a polynomial over the integers. Factor[poly, 
Modulus->p] factors a polynomial modulo a prime p. Factor[poly, 
Extension->{a1, a2, ... }] factors a polynomial allowing coefficients that 
are rational combinations of the algebraic numbers ai. "

Times @@ (x-(Re[#]+I*Im[#]& /@ (x /. Solve[1 + x^4 == 0, x])))

(x - (1 + I)/Sqrt[2])*(x - (1 - I)/Sqrt[2])*
  (x + (1 - I)/Sqrt[2])*(x + (1 + I)/Sqrt[2])

%//Simplify

x^4 + 1


Bob Hanlon

In a message dated 2001/1/25 1:40:30 AM, k5gj at earthlink.net writes:

>I would like to factor 1+x^4.   Mathematica 3 will only respond with
>In[1]:= Factor[1+x^4]
>Out[2]= 1+x^4
>
>
>    Other systems will give the complex result
>
>1+x^4 = (x+1/2*Sqrt(2)*I+1/2*Sqrt(2))*
>        (x+1/2*Sqrt(2)*I-1/2*Sqrt(2))*
>        (x-1/2*Sqrt(2)*I+1/2*Sqrt(2))*
>        (x-1/2*Sqrt(2)*I-1/2*Sqrt(2))
>
>
>    How would I factor 1+x^4 with Mathematica
>


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