#11891: NumberField(...).pari_polynomial() should return an integral polynomial
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Reporter: jdemeyer | Owner: davidloeffler
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.7.3
Component: number fields | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author: Jeroen Demeyer
Merged: | Dependencies:
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Changes (by jdemeyer):
* status: needs_review => needs_work
Comment:
Replying to [comment:3 was]:
> The code looks good, and passes tests, and it means we can at least
compute discriminants.
>
> The first and second things I try still don't work though, and I'm
curious what you think about this:
> {{{
> sage: k.<a, c> = NumberField([x^2 + 1/3, x^2 + 1/4])
> sage: k
> Number Field in a with defining polynomial x^2 + 1/3 over its base field
> sage: a+c
> *** Warning: non-monic polynomial. Result of the form [nf,c].
> ERROR: An unexpected error occurred while tokenizing input
> ...
> BOOM!
> sage: k.relative_discriminant()
> *** Warning: non-monic polynomial. Result of the form [nf,c].
> BOOM!
> }}}
>
>
> Side Remarks: 1. I've always intended to just rewrite number fields to
completely use
> {{{
> sage.schemes.elliptic_curves.heegner.make_monic
> }}}
> behind the scenes, and do *everything* that involves PARI in all cases
using a monic integral polynomial, and only convert to the user's
representation for input and output. I wish I had done that when I was
first writing number fields.
I never intended this ticket to completely fix non-integral/non-monic
number fields. I can have a look at the error messages above and try to
fix them, but I also do not want to put too much effort. The main
motivation for this ticket was to support #11890, for which it seems to
work.
> 2. This is disturbing:
> {{{
> sage: K.<I> = NumberField(x^2+1)
> sage: K.pari_polynomial()
> x^2 + 1
> sage: K.pari_polynomial('I')
> 0
> }}}
> I would rather get an error message in the latter case.
Okay, that should be fixable (currently, we simply substitute instead of
creating a polynomial with a given variable).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11891#comment:4>
Sage <http://www.sagemath.org>
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