#252: Make number fields work when polynomial not integral or not monic.
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Reporter: was | Owner: davidloeffler
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: number fields | Resolution:
Keywords: | Merged in:
Authors: Peter Bruin | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/pbruin/252-number_fields | fce3c709dbeb1b7073b432527fe31a53eb7b8124
Dependencies: #18740 | Stopgaps:
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Changes (by pbruin):
* status: new => needs_review
Old description:
> Make number fields work when polynomial not integral or not monic.
>
> {{{
> sage: R.<x> = QQ[]
> sage: L.<b> = NumberField(x^2-1/2)
> sage: L.discriminant()
> Traceback (most recent call last):
> ...
> gen.PariError: (8)
> }}}
New description:
The goal of this ticket is to make number fields work when the defining
polynomial is not integral or not monic.
If the user specifies a non-integral or non-monic polynomial to define an
absolute or relative number field, we define the corresponding PARI number
field by a monic integral polynomial obtained from the PARI functions
`polredbest` and `rnfpolredbest`, respectively.
The new methods `NumberField_generic._pari_absolute_structure()` and
`NumberField_relative._pari_relative_structure()` return the data needed
to convert elements between the Sage `NumberField` and the PARI `nf`
structure.
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Ticket URL: <http://trac.sagemath.org/ticket/252#comment:23>
Sage <http://www.sagemath.org>
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