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