http://mathworld.wolfram.com/RootofUnity.html seem to indicate you are right.
R.E. Boss > Date: Mon, 2 Jun 2014 13:59:10 -0600 > From: [email protected] > To: [email protected] > Subject: Re: [Jprogramming] Identifying roots of unity > > Is n below a primitive root of unity? > > n=._1^3r8 > > *./2 x:(12 o. n)%o.2 > > 48 > > n^48 > > 1j_3.9968e_15 > > > Yes. > > > On Mon, Jun 2, 2014 at 1:42 PM, Don Guinn <[email protected]> wrote: > > > I don't think that this is a complete test. If 1~:|n then it it is not a > > primitive root of unity. But n must be a complex number when raised to an > > *integer* power is 1. Maybe converting the complex number to polar then > > checking the angle and seeing if it is a rational fraction of a circle. > > > > Obviously computers will always find some rational number though it might > > require raising n to a very large power. There should be some reasonable > > limit as to how large the power may be. > > > > > > On Mon, Jun 2, 2014 at 1:08 PM, Raul Miller <[email protected]> wrote: > > > >> 1=|n > >> > >> Thanks, > >> > >> -- > >> Raul > >> > >> > >> On Mon, Jun 2, 2014 at 2:54 PM, Dan Bron <[email protected]> wrote: > >> > Given a complex number, how can I determine whether it is a primitive > >> root > >> > of unity? > >> > > >> > (This is a subtask of a code golf problem, so the shorter the better) > >> > > >> > -Dan > >> > ---------------------------------------------------------------------- > >> > For information about J forums see http://www.jsoftware.com/forums.htm > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm > >> > > > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
