I'm not sure what your example of rug means.
ruq i:2
0 1 0 1 0
Isn't this always true?
y=:13
((ruq i:y)-:((1=i:y)+.(_1=i:y)))
1
y=:14
((ruq i:y)-:((1=i:y)+.(_1=i:y)))
1
Linda
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Cliff Reiter
Sent: Monday, June 02, 2014 9:17 PM
To: [email protected]
Subject: Re: [Jprogramming] Identifying roots of unity
In light of the link provided by R.E.Boss and x: on complex numbers
x: 1j1
|domain error
| x:1j1
|[-0]
We might define rational query as occurring when the denominator of the
rationalization is small and not an error
ratq=:(1e8>{:@:(2&x:)) :: 0:"0
ratq ?10$0
0 0 0 0 0 0 0 0 0 0
ratq 1001%~i.10
1 1 1 1 1 1 1 1 1 1
ratq 1 j. i.10
1 0 0 0 0 0 0 0 0 0
Then a number is a root of unity if its log divided by 2 pi i is rational
ruq=:ratq@:(0j2p1%~^.)
ruq i:2
0 1 0 1 0
ruq ^0j2p1 * (i.%[)13
1 1 1 1 1 1 1 1 1 1 1 1 1
ruq ?10$0
0 0 0 0 0 0 0 0 0 0
Obviously limited by floating precision. Other limitations??
Best, Cliff
On 6/2/2014 5:55 PM, R.E. Boss 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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>>>> ----------------------------------------------------------------------
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>>>>
>>>
>> ----------------------------------------------------------------------
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>
> ----------------------------------------------------------------------
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>
--
Clifford A. Reiter
Lafayette College, Easton, PA 18042
http://webbox.lafayette.edu/~reiterc/
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