Hi,
On Mon, May 21, 2012 at 9:29 AM, Oleksandr Kazymyrov
<vrona.aka.ham...@gmail.com> wrote:
> I have encountered the following problem In Sage 5.0:
> sage: R.<x>=ZZ[]
> sage: k=GF(2^8,name='a',modulus=x^8+x^4+x^3+x+1)
> sage: k(ZZ(3).digits(2))
> a + 1
> sage: k.gen()^ZZ(k(ZZ(3).digits(2)).log_repr())
> a
> sage: k.gen()^ZZ(k(ZZ(3).digits(2)).log_repr()) == k(ZZ(3).digits(2))
> False
> sage: k("a+1")^ZZ(k(ZZ(3).digits(2)).log_repr()) == k(ZZ(3).digits(2))
> True
>
> It easy see that k.gen() or k.multiplicative_generator() is not a generator
> of the finite field:
> sage: k.multiplicative_generator()
> a^4 + a + 1
Why is it clear that a^4+a+1 is not a multiplicative generator? I think it is:
sage: k.<a> = GF(2^8, names='a', name='a', modulus=x^8+x^4+x^3+x+1)
sage: (a^4+a+1).multiplicative_order()
255
Indeed, so is a+1:
sage: (a+1).multiplicative_order()
255
The docs for multiplicative_generator() say: "return a generator of
the multiplicative group", then add "Warning: This generator might
change from one version of Sage to another."
--
Best,
Alex
--
Alex Ghitza -- Lecturer in Mathematics -- The University of Melbourne
http://aghitza.org
--
To post to this group, send email to sage-support@googlegroups.com
To unsubscribe from this group, send email to
sage-support+unsubscr...@googlegroups.com
For more options, visit this group at
http://groups.google.com/group/sage-support
URL: http://www.sagemath.org
