Re: Factor[1+x^4]

• To: mathgroup at smc.vnet.net
• Subject: [mg26865] Re: Factor[1+x^4]
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Fri, 26 Jan 2001 01:27:16 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <94ojm5\$emb@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

In[]:=Factor[1 + x^4, Extension -> {1/Sqrt[2], I/Sqrt[2]}]

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

BTW: Other systems ?? There are other systems, I'm puzzled.

Regards
Jens

Tom Cage wrote:
>
> 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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