On 4 May 2015 at 15:22, Evrim Ulu <evrim...@gmail.com> wrote: > > Here it is: > > F16.extension(modulus=x^7+x+1)
To quote from the documentation of the extension() method used here: "Extensions of non-prime finite fields by polynomials are not yet supported: we fall back to generic code:" follwed by an example. In your case you get Univariate Quotient Polynomial Ring in x over Finite Field in g of size 2^4 with modulus x^7 + x + 1 which does at least know that it is a field, but its type is not FiniteField but PolynomialQuatientRing . There has been recent work to improve handling of relative extensions of finite fields, and perhaps someone who has been involved with that will comment further. John Cremona > > > On Monday, May 4, 2015 at 5:02:52 PM UTC+3, Evrim Ulu wrote: >> >> Hello, >> >> I'm having trouble extending a finite field. Any help would be >> appreciated. >> >> F16 = GF(16, 'g') >> F16_x.<x> = PolynomialRing(F16, 'x') >> HH = GF(F16^7, modulus=x^7 + x + 1, name='h') >> >> I basically try to extend 2^4 to 2^4*7 with a degree 7 irreducible. >> I get the following. >> >> best, >> evrim. >> >> >> sage: HH = FiniteField(F16^7, modulus=x^7 + x + g^15, name='h') >> >> --------------------------------------------------------------------------- >> TypeError Traceback (most recent call >> last) >> /usr/lib/sagemath/local/lib/python2.7/site-packages/sage/all_cmdline.pyc >> in <module>() >> ----> 1 HH = FiniteField(F16**Integer(7), modulus=x**Integer(7) + x + >> g**Integer(15), name='h') >> >> /usr/lib/sagemath/src/sage/structure/factory.pyx in >> sage.structure.factory.UniqueFactory.__call__ >> (build/cythonized/sage/structure/factory.c:1207)() >> 362 False >> 363 """ >> --> 364 key, kwds = self.create_key_and_extra_args(*args, **kwds) >> 365 version = self.get_version(sage_version) >> 366 return self.get_object(version, key, kwds) >> >> >> /usr/lib/sagemath/local/lib/python2.7/site-packages/sage/rings/finite_rings/constructor.pyc >> in create_key_and_extra_args(self, order, name, modulus, names, impl, proof, >> check_irreducible, **kwds) >> 426 proof = arithmetic() >> 427 with WithProof('arithmetic', proof): >> --> 428 order = Integer(order) >> 429 if order <= 1: >> 430 raise ValueError("the order of a finite field must >> be at least 2") >> >> /usr/lib/sagemath/src/sage/rings/integer.pyx in >> sage.rings.integer.Integer.__init__ >> (build/cythonized/sage/rings/integer.c:6020)() >> 688 return >> 689 >> --> 690 raise TypeError, "unable to coerce %s to an >> integer" % type(x) >> 691 >> 692 def __reduce__(self): >> >> TypeError: unable to coerce <class >> 'sage.modules.free_module.FreeModule_ambient_field_with_category'> to an >> integer >> > -- > 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. -- 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.