Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2001
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2001

[Date Index] [Thread Index] [Author Index]

Search the Archive

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
>
>
>




  • Prev by Date: Re: Overriding Power
  • Next by Date: Re: Who can help me?
  • Previous by thread: Re: Factor[1+x^4]
  • Next by thread: Re: reference