#11891: NumberField(...).pari_polynomial() should return an integral polynomial
-----------------------------+----------------------------------------------
Reporter: jdemeyer | Owner: davidloeffler
Type: enhancement | Status: needs_review
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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Comment(by 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.
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. What do you
think? If you agree, could you open a ticket?
Anyway, I'll wait for your comments...
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11891#comment:3>
Sage <http://www.sagemath.org>
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