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 >