       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)*(x - (1 - I)/Sqrt)*
(x + (1 - I)/Sqrt)*(x + (1 + I)/Sqrt)

%//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:= Factor[1+x^4]
>Out= 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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