Hi Jan, hi John,

On 2014-05-04, John Cremona <[email protected]> wrote:
> On 4 May 2014 13:20, Jan Medina <[email protected]> wrote:
>> I wan to calculate log(\theta+i,\theta) for i in a finte field and theta a
>> primtive element
>>
>
> You can see the documentation of this function like this:
>
> sage: F=GF(101)
>                                      sage: a=F(3)
>
>       sage: a.log?
>
> and even the code using a.log??

I somehow have the impression that part of the problem is that John
thinks in terms of methods ( a.log() ), while Jan is thinking in terms
of functions ( log(a) ).

Anyway, the documentation of the *function* "log" can be seen with
  sage: log?
and the source code with
  sage: log??

And it seems to be the case that ultimately the function call log(a)
will end up with the method call a.log(). So, answering Jan's question:
Yes, if alpha is is an element of a finite field with primitive element
theta, then log(alpha,theta) is essentially the same as directly calling
alpha.log(theta), and this the discrete logarithm.

Best regards,
Simon


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