Here it is:
F16.extension(modulus=x^7+x+1)
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
>
>
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