Re: Factor[1+x^4]
- To: mathgroup at smc.vnet.net
- Subject: [mg26882] Re: Factor[1+x^4]
- From: "Allan Hayes" <hay at haystack.demon.co.uk>
- Date: Fri, 26 Jan 2001 01:27:27 -0500 (EST)
- References: <94ojm5$emb@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Tom,
Factor[1 + x^4, Extension ->
ComplexExpand[Flatten[x /. Solve[1 + x^4 == 0, x]]]]
(1*(Sqrt[2] - (1 + I)*x)*(Sqrt[2] - (1 - I)*x)*
(Sqrt[2] + (1 - I)*x)*(Sqrt[2] + (1 + I)*x))/4
Factor[1 + x^4, Extension -> {I, Sqrt[2]}]
(1*(Sqrt[2] - (1 + I)*x)*(Sqrt[2] - (1 - I)*x)*
(Sqrt[2] + (1 - I)*x)*(Sqrt[2] + (1 + I)*x))/4
Factor[1 + x^4, Extension -> {I}]
(-I + x^2)*(I + x^2)
Factor[1 + x^4, Extension -> {Sqrt[2]}]
-(-1 + Sqrt[2]*x - x^2)*(1 + Sqrt[2]*x + x^2)
--
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565
"Tom Cage" <k5gj at earthlink.net> wrote in message
news:94ojm5$emb at smc.vnet.net...
> 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
>
>
>