On 4 May 2014 13:20, Jan Medina <janmedin...@gmail.com> wrote:
> But the log() function works on a finite field too. So its not correct if a
> i use the log on finite fields?
OK -- you did not explain at all what is was that you were doing, na d
I could not guess!
>
> 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??, which reveals that in prime fields it
calls the pari library while in the general case it uses the
discrete_log function which is a completely generic implementation
(using either baby-step-giant-step or rho), hence fine for
small-medium fields but no good for large ones.
e.g.
sage: F=GF(101^3,'a')
sage: theta = F.primitive_element()
sage: [log(theta+i,theta) for i in range(10)]
[1, 596770, 963004, 681797, 310936, 434845, 968831, 682947, 790282, 125599]
John
>
> 2014-05-04 6:07 GMT-05:00 John Cremona <john.crem...@gmail.com>:
>>
>> log() is a function you would apply to numbers, say real or complex:
>>
>> sage: a = RealField(100)(2)
>> sage: a.log()
>> 0.69314718055994530941723212146
>>
>> while discrete_log() is something to do in a finite cyclic group. For
>> example:
>>
>> sage: F = FiniteField(101)
>> sage: a = F(2)
>> sage: b = a^67
>> sage: discrete_log(b,a)
>> 67
>>
>> John
>>
>> On 4 May 2014 02:17, Jan Medina <janmedin...@gmail.com> wrote:
>> > Hi everybody.
>> >
>> > I want to know what algorithm are implemented for calculate log() and
>> > discrete log(). and what are the differences?
>> >
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