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
> > >> >
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