One more question If I may ask. Is there a way to get the minimal poly of some conjugates over GF(2^4)? I always end up degree 28 in this case, i want to see some of degree 7. I've tried to embed it into GF(2^4)[x] and factor yet no luck.
Best, evrim. 2015-05-04 20:04 GMT+03:00 Evrim Ulu <evrim...@gmail.com>: > Thats right f(g(x)) is not irreducible obviously, shame on me. > > I did this to get the order: > sage: (k[x](x^7+x+1)).roots()[0][0].multiplicative_order() > 127 > > First root, multiplicative order. > > The real confusion comes from the notation I guess. When you said > k[x](x^7+x+1) i obviously thought we are generating an Ideal. This is > obviously untrue since k[x]() is a function who casts it into the > ring. > > This is really confusing, Thanks for your help. > > best, > evrim. > > > 2015-05-04 18:27 GMT+03:00 Nils Bruin <nbr...@sfu.ca>: >> On Monday, May 4, 2015 at 7:58:19 AM UTC-7, Evrim Ulu wrote: >>> >>> I see that, thanks for the info. >>> >>> Actually F16.extension(..).gen().multiplicative_order() gives >>> NotImplementedError >>> >>> So basically, if i want to simulate the behaviour I can take two poly >>> f(x), g(x) and generate a field using modulus f(g(x)) composition i >>> guess. >> >> >> Only if you care about having that basis (is f(g(x)) guaranteed to be >> irreducible?) You can also just construct k=GF(2^(4*7),'a') and hope the >> underlying library takes a smart choice for its generator. You can then see >> how GF[x]/(x^7+x+1) embeds by asking for (k[x](x^7+x+1)).roots() >> >> -- >> You received this message because you are subscribed to a topic in the >> Google Groups "sage-support" group. >> To unsubscribe from this topic, visit >> https://groups.google.com/d/topic/sage-support/mVoFYqsfAAY/unsubscribe. >> To unsubscribe from this group and all its topics, send an email to >> sage-support+unsubscr...@googlegroups.com. >> To post to this group, send email to sage-support@googlegroups.com. >> Visit this group at http://groups.google.com/group/sage-support. >> For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
