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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