On 17 mar, 10:13, John Cremona <john.crem...@gmail.com> wrote:
> 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

This is now #8558, for the gcd, it seems that a simple:

sage: f = SomeField.random_element()
sage: f1 = pari([i._pari_('y') for i in f.list()]).Pol()

is a valid pari representation of f.

This, or something similar, should be implemented for absolute number
fields. I will look form problems this weekend and submit a patch.

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