#252: Make number fields work when polynomial not integral or not monic.
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Reporter: was | Owner: davidloeffler
Type: defect | Status: new
Priority: major | Milestone: sage-6.4
Component: number fields | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by pbruin):
In !SageMath 6.7.beta1:
{{{
sage: R.<x> = QQ[]
sage: L.<b> = NumberField(x^2-1/2)
sage: L.discriminant()
8
sage: L.ring_of_integers()
Maximal Order in Number Field in b with defining polynomial x^2 - 1/2
}}}
However, there are still problems; see e.g. #18243. We should make use of
the fact that when one feeds a non-monic or non-integral polynomial `f` to
PARI's `nfinit()`, it returns a pair `[nf, c]` where `nf` is an number
field isomorphic to '''Q'''[''x'']/(''f'') and defined by a monic integral
polynomial, and `c` is a root of `f` in `nf`.
--
Ticket URL: <http://trac.sagemath.org/ticket/252#comment:17>
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