Hi again,
A try to use *log* function and got error:
sage: R.<x>=ZZ[]
sage: k.<a>=GF(2^8,modulus=x^8+x^4+x^3+x+1)
sage: b=k.random_element()
sage: b.log(a)
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
/home/hamsin/<ipython console> in <module>()
/home/hamsin/bin/sage/local/lib/python2.7/site-packages/sage/rings/finite_rings/element_givaro.so
in sage.rings.finite_rings.element_givaro.FiniteField_givaroElement.log
(sage/rings/finite_rings/element_givaro.cpp:11248)()
/home/hamsin/bin/sage/local/lib/python2.7/site-packages/sage/groups/generic.pyc
in discrete_log(a, base, ord, bounds, operation, identity, inverse, op)
814 return CRT_list(l,[pi**ri for pi,ri in f])
815 except ValueError:
--> 816 raise ValueError, "No discrete log of %s found to base
%s"%(a,base)
817
818 def discrete_log_generic(a, base, ord=None, bounds=None,
operation='*', identity=None, inverse=None, op=None):
ValueError: No discrete log of a^7 + a^6 + a^5 + a^4 + a^2 + 1 found to
base a
I also found some strangeness:
sage: m=[a^i for i in xrange(255)]
sage: m.append(0)
sage: len(set(m))
52
But last value must be 256, if *a *is a generator. So *k.gens() *returns
wrong value.
P.S.
sage: version()
'Sage Version 5.0, Release Date: 2012-05-14'
On Monday, May 21, 2012 1:29:29 AM UTC+2, Oleksandr Kazymyrov wrote:
>
> Hello all.
>
> 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
> sage: k.gen()
> a
> sage: k.list()
> [0, a + 1, a^2 + 1, a^3 + a^2 + a + 1, a^4 + 1, a^5 + a^4 + a + 1, a^6 +
> a^4 + a^2 + 1, ... ]
>
> Generator is "a+1"!
>
> How to get generator of Finite Field? It was fine in Sage 4.8.
>
> Ubuntu 12.04
> Linux hamsin 3.2.0-24-generic #37-Ubuntu SMP Wed Apr 25 08:43:52 UTC 2012
> i686 i686 i386 GNU/Linux
>
> Best regards,
> Oleksandr
>
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