For an example of how polynomials over number fields are converted
into pari polynomials, see
sage/rings/polynomial/polynomial_element.pyx, in the factor function.
This is the code already used to factor polynomials over number fields
by converting to pari. It is more complicated than one would like for
a couple of reasons: getting round bugs in pari's factorization of
non-monic polynomials, and variable names.
One has to be rather careful because of the variable names, here both
the name of the number field generator and the name of the polynomial
generator, since pari will only work if these are suitable.
John
On 16 March 2010 22:55, luisfe <lftab...@yahoo.es> wrote:
>
>
> On 16 mar, 23:27, daveloeffler <dave.loeff...@gmail.com> wrote:
>> Can you give an example where polynomials are being passed incorrectly
>> to Pari? There are some known bugs in Pari's own factorisation
>> routines (fixed in Pari 2.3.5, which should hopefully be in the next
>> Sage release), but if there are problems translating between Pari and
>> Sage polynomials that's worrying.
>
> My error, there is no coercion for this class
>
> sage: N=NumberField(x^2-2,'a')
> sage: K=N['t']
> sage: f=K.random_element()
> sage: pari(f)
> ---------------------------------------------------------------------------
> PariError Traceback (most recent call
> last)
>
> /home/luisfe/<ipython console> in <module>()
>
> /opt/SAGE/sage/local/lib/python2.6/site-packages/sage/libs/pari/gen.so
> in sage.libs.pari.gen.PariInstance.__call__ (sage/libs/pari/gen.c:
> 38930)()
>
> /opt/SAGE/sage/local/lib/python2.6/site-packages/sage/rings/polynomial/
> polynomial_element.so in
> sage.rings.polynomial.polynomial_element.Polynomial._pari_ (sage/rings/
> polynomial/polynomial_element.c:26227)()
>
> /opt/SAGE/sage/local/lib/python2.6/site-packages/sage/rings/polynomial/
> polynomial_element.so in
> sage.rings.polynomial.polynomial_element.Polynomial._pari_with_name
> (sage/rings/polynomial/polynomial_element.c:26353)()
>
> /opt/SAGE/sage/local/lib/python2.6/site-packages/sage/libs/pari/gen.so
> in sage.libs.pari.gen._pari_trap (sage/libs/pari/gen.c:44387)()
>
> PariError: (8)
>
>
> I think that I was first trying some naive transformation like
> L = [pari(i) for i in f.list()]
> add([L[i]*pari('t')^i for i in range(f.degree())])
>
> And confused this with the actual coercion model.
>
> --
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