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MathGroup Archive 2001

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Re: Factor[1+x^4]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg26862] Re: [mg26855] Factor[1+x^4]
  • From: "Carl K. Woll" <carlw at u.washington.edu>
  • Date: Fri, 26 Jan 2001 01:27:14 -0500 (EST)
  • References: <200101250613.BAA14708@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Tom,

In Mathematica 4 you can do

Factor[1+x^4, Extension->{2^(1/2),I}]

((Sqrt[2] - (1 + I) x) (Sqrt[2] - (1 - I) x) (Sqrt[2] + (1 - I) x) 
 
    (Sqrt[2] + (1 + I) x)) / 4

I don't have 3.0 anymore to compare.

Carl Woll
Physics Dept
U of Washington

----- Original Message ----- 
From: "Tom Cage" <k5gj at earthlink.net>
To: mathgroup at smc.vnet.net
Subject: [mg26862] [mg26855] Factor[1+x^4]


> 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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