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Re: Factor[1+x^4]
*To*: mathgroup at smc.vnet.net
*Subject*: [mg26870] Re: [mg26855] Factor[1+x^4]
*From*: BobHanlon at aol.com
*Date*: Fri, 26 Jan 2001 01:27:19 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
?Factor
"Factor[poly] factors a polynomial over the integers. Factor[poly,
Modulus->p] factors a polynomial modulo a prime p. Factor[poly,
Extension->{a1, a2, ... }] factors a polynomial allowing coefficients that
are rational combinations of the algebraic numbers ai. "
Times @@ (x-(Re[#]+I*Im[#]& /@ (x /. Solve[1 + x^4 == 0, x])))
(x - (1 + I)/Sqrt[2])*(x - (1 - I)/Sqrt[2])*
(x + (1 - I)/Sqrt[2])*(x + (1 + I)/Sqrt[2])
%//Simplify
x^4 + 1
Bob Hanlon
In a message dated 2001/1/25 1:40:30 AM, k5gj at earthlink.net writes:
>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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