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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