You can generate roots of unity with this: ([: r. 2 * (o.@:%~ i.)) . EG ([: r. 2 * (o.@:%~ i.)) 3 1 _0.5j0.866025 _0.5j_0.866025
On Mon, Jun 2, 2014 at 6:33 PM, Raul Miller <[email protected]> wrote: > Proof that I am wrong. (And, that - if it's understandable that the > information on the wolfram page leads to my implementation of rootsN that > it is significantly incomplete.): > > p. 1 1 1 > ┌─┬────────────────────────────┐ > │1│_0.5j0.866025 _0.5j_0.866025│ > └─┴────────────────────────────┘ > |1{::p. 1 1 1 > 1 1 > > Like I said... I'm really good at being wrong. Or, something like that. > > Thanks, > > -- > Raul > > > On Mon, Jun 2, 2014 at 5:55 PM, R.E. Boss <[email protected]> wrote: > > > 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 > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > -- Devon McCormick, CFA ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
