Factor question

*To*: mathgroup at smc.vnet.net*Subject*: [mg71270] Factor question*From*: "dimitris" <dimmechan at yahoo.com>*Date*: Sun, 12 Nov 2006 06:48:22 -0500 (EST)

Why Factor gives the follwing output below? sols = x /. Solve[x^6 - 1 == 0] {-1, 1, -(-1)^(1/3), (-1)^(1/3), -(-1)^(2/3), (-1)^(2/3)} Factor[x^6 - 1, Extension -> %] (-1 + (-1)^(1/3) - x)*((-1)^(1/3) - x)*(-1 + x)*(1 + x)*(-1 + (-1)^(1/3) + x)*((-1)^(1/3) + x) that is why it writes e.g. (-1 + (-1)^(1/3) instead of (-1)^(2/3) Block[{Message}, FullSimplify[(-1)^(2/3) == -1 + (-1)^(1/3)]] True How is possible to get with Factor the output as follows? Times @@ Apply[Plus, Solve[x^6 - 1 == 0], 2] (-1 + x)*(1 + x)*(-(-1)^(1/3) + x)*((-1)^(1/3) + x)*(-(-1)^(2/3) + x)*((-1)^(2/3) + x) or Times @@ Apply[Plus, Flatten[Solve[x^6 - 1 == 0], 1], {1}] (-1 + x)*(1 + x)*(-(-1)^(1/3) + x)*((-1)^(1/3) + x)*(-(-1)^(2/3) + x)*((-1)^(2/3) + x)] Regards Dimitris