Today is easiest way and *secure* to use multiplicative_generator function:
sage: K=GF(2^4,'a')
sage: K
Finite Field in a of size 2^4
sage: b=K.random_element()
sage: b.log(K.multiplicative_generator())
14
sage: K.multiplib.log(K.multiplicative_generator())
K.multiplication_table K.multiplicative_generator
sage: K.multiplicative_generator()^b.log(K.multiplicative_generator()) == b
True
Because the function log_repr() works only in some special cases.
sage: K=GF(2^4,'a',modulus=ZZ['x']('x^4 + x^3 + x^2 + x + 1'));
sage: K.list()
[0, a + 1, a^2 + 1, a^3 + a^2 + a + 1, a^3 + a^2 + a, a^3 + a^2 + 1, a^3,
a^2 + a + 1, a^3 + 1, a^2, a^3 + a^2, a^3 + a + 1, a, a^2 + a, a^3 + a, 1]
sage: b=K.random_element()
sage: b
a^3 + a
sage: b.log_repr()
'14'
sage: b^ZZ(b.log_repr()) == b
False
sage: K.multiplicative_generator()
a^2 + a + 1
sage: K.multiplicative_generator()^ZZ(b.log(K.multiplicative_generator()))
== b
True
On Monday, September 17, 2012 11:07:58 PM UTC+2, Mike OS wrote:
>
> HI
>
> I was asking myself this question and couldn't find an answer in the
> documentation, not
> in past posts (which is how I found this email).
>
> So I re-ask the question is there a way to have finite field elements
> printed as powers of the primitive element?
>
> Thanks
>
> Mike
>
> On Saturday, October 31, 2009 2:34:38 AM UTC-7, Kwankyu wrote:
>>
>> Hi,
>>
>> Is it possible to get elements of a finite field printed as powers of
>> a primitive element if the modulus is a primitive polynomial? That
>> will save a lot of screen space.
>>
>>
>> Kwankyu
>
>
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