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Re: Factor[1+x^4]


In my opinion at least, Mathematica does the right thing and requires you to
specify the extension of the rationals over which you want to factor. This
way is  more flexible and powerful:


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

Out[1]=
       2        2
(-I + x ) (I + x )

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

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

and so on

-- 
Andrzej Kozlowski
Toyama International University
JAPAN

http://platon.c.u-tokyo.ac.jp/andrzej/
http://sigma.tuins.ac.jp/


on 01.1.25 3:13 PM, Tom Cage at k5gj at earthlink.net 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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