I think the DFT stuff in SAGE is not in the tutorial or reference manual
but documentation does exist. First, the CFT links on
http://sage.math.washington.edu/home/wdj/teaching/index.html
have many examples. Second, if you go to
devel/sage-main/sage/gsl/dft.py file, you'll find lots of examples
in the docstrings.
If you have questions or comments, let me know.
++++++++++++++++++++++++++++++++++++++++++
[EMAIL PROTECTED] wrote:
> Hi David,
>
> I installed SAGE and as you pointed out it takes a while to get around it.
> It looks like it can do loads of things so thank you for pointing it out to
> me.
>
> I am currently going through the tutorials, could you point me to the best
> sections to read for my particular problem, namely DFT for arbitrary length
> sequences over finite fields.
>
> Many thanks for your help,
> Alexandra.
>
> Quoting David Joyner <[EMAIL PROTECTED]>:
>
>> SAGE can handle that case, though the documentation is hard
>> to find so please let me know if you have questions or comments.
>>
>> As far as GAP is concerned, if N is the period of your sequence
>> f = {f_j}, j >= 0 and f_j in F=GF(q), then to define a DFT of f,
>> you are going to have to have an embedding of ZZ/NZZ into
>> GF(q)^x. This embedding gives you a "natural" choice for the
>> generator of ZZ/NZZ: Take it to have generator g = Z(q)^d,
>> where d = (q-1)/N.
>>
>> ++++++++++++++++++++++++++++++++++++++
>>
>>
>> On 5/27/07, Alexandra Alecu <[EMAIL PROTECTED]> wrote:
>>> Hello David,
>>>
>>> Thank you very much for your reply.
>>>
>>> I am wondering though, what can I do when q is not a prime power.
>>> Specifically in my case for the DFT of a sequence of period N
>>> (arbitrary), when the sequence has a period N which is not p^m-1, how
>>> can i find a primitive n-th root of unity?
>>>
>>> I will download the SAGE and try it.
>>>
>>> Thanks and Regards,
>>> Alexandra.
>>>
>>> On Sun, 2007-05-27 at 17:08 -0400, David Joyner wrote:
>>>> Z(q) (q a prime power) is a generator of the finite field GF(q)
>>>> and a generator of the (cyclic) group GF(q)^x.
>>>>
>>>> ++++++++++++++++++++++++++
>>>>
>>>> On 5/27/07, [EMAIL PROTECTED] <[EMAIL PROTECTED]> wrote:
>>>>> Dear forum
>>>>>
>>>>> I have the following problem: I need to implement the Discrete
>> Fourier
>>>>> Transform on arbitrary finite fields.
>>>>>
>>>>> Basically starting from a sequence s of period N over a finite
>> field F and
>>>>> having a primitive n-th root of unity \alpha within that field F, I
>> need to
>>>>> calculate the transformed sequence S over the extension field of F
>> which
>>>>> contains all the powers of \alpha. Each term of S is a sum of terms
>> of s
>>>>> multiplied with powers of \alpha.
>>>>>
>>>>> Anyway... my problem is (and it might be an easy one) how to find
>> the
>>>>> primitive n-th root of unity in a finite field?
>>>>> I noticed that for the complex numbers I could use E(n), I need
>> something
>>>>> similar for a finite field.
>>>>>
>>>>> All I have at the moment is a way to find the primitive n-th root
>> of unity
>>>>> for the cases when n = p^m - 1 where p is a prime and m > 1. For
>> this I use
>>>>> the PrimitiveRoot(GF(p^m)) which returns the primitive root of the
>> finite
>>>>> field GF(p^m).
>>>>>
>>>>> Please can I have your suggestions on how I should solve this
>> problem.
>>>>> Alternatively could you point me to an existing implementation of
>> the
>>>>> Discrete Fourier Transform over finite fields.
>>>>>
>>>>> Thank you for your help in anticipation.
>>>>>
>>>>> Kind regards,
>>>>> Alexandra
>>>>>
>>>>> ------
>>>>> Alexandra Alecu
>>>>> Research Student
>>>>>
>>>>> Department of Computer Science
>>>>> Holywell Park
>>>>> Loughborough University
>>>>> Loughborough, LE11 3TU
>>>>> England
>>>>> Telephone +44 (0)1509 635717
>>>>> Internal extn 5720
>>>>> Fax +44 (0)1509 635722
>>>>> E-mail A.Alecu at lboro.ac.uk
>>>>>
>>>>> _______________________________________________
>>>>> Forum mailing list
>>>>> [EMAIL PROTECTED]
>>>>> http://mail.gap-system.org/mailman/listinfo/forum
>>>>>
>>>
>
>
>
>
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