On Tue, Oct 14, 2008 at 7:02 AM, Peter Schwabe <[EMAIL PROTECTED]> wrote:
> Hi,
>
> I just encountered a problem with the is_irreducible function. The
> following code does not work as exptected:
>
> p =
> 82434016654300679721217353503190038836571781811386228921167322412819029493183
> F = GF(p)
>
> Fu.<u> = F[]
> Fext2.<X> = GF(p**2, name='X', modulus=u**2 + 2)
> xi = X + 1
>
> Fext2v.<v> = Fext2[]
> Fext6.<Y> = GF(p**6, name='Y', modulus=v**3 - xi)
>
> Fext6w.<w> = Fext6[]
>
> f = w**2 - Y
> f.is_irreducible()
At this point one gets:
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/home/wstein/.sage/sage_notebook/worksheets/admin/2/code/10.py",
line 8, in <module>
f.is_irreducible()
File
"/home/wstein/sage/local/lib/python2.5/site-packages/SQLAlchemy-0.4.6-py2.5.egg/",
line 1, in <module>
File "polynomial_element.pyx", line 3876, in
sage.rings.polynomial.polynomial_element.Polynomial.is_irreducible
(sage/rings/polynomial/polynomial_element.c:25707)
File "polynomial_element.pyx", line 2061, in
sage.rings.polynomial.polynomial_element.Polynomial.factor
(sage/rings/polynomial/polynomial_element.c:15667)
File "gen.pyx", line 7893, in sage.libs.pari.gen._pari_trap
(sage/libs/pari/gen.c:37972)
sage.libs.pari.gen.PariError: sorry, (15)
Which is PARI's (the library used by Sage for this) way of saying it
doesn't know how to do the relevant polynomial factorization. So
this is a NotImplementedError, really.
Somebody should think this through some more and open a ticket for what exactly
needs to be implemented. Maybe somebody whose working on finite
fields anyways...
William
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