#4738: base_ring of orders in relative number fields is wrong
-------------------------------------+-------------------------------------
Reporter: ncalexan | Owner: davidloeffler
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.2
Component: number fields | Resolution:
Keywords: base ring | Merged in:
relative number field order | Reviewers:
Authors: Alex Ghitza | Work issues:
Report Upstream: N/A | Commit:
Branch: | 2b459322c84d9dac7087eb30f1db4b73db6ccb8c
u/AlexGhitza/ticket/4738 | Stopgaps:
Dependencies: |
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Changes (by pbruin):
* commit: => 2b459322c84d9dac7087eb30f1db4b73db6ccb8c
* upstream: => N/A
Comment:
Do we really want the ''maximal'' order of the base field? I would say
the base ring should be the intersection of the relative order with the
base field. In the following example, the order ''R'' in ''L'' does not
contain the maximal order of ''K'':
{{{
sage: K.<s> = QuadraticField(5)
sage: O = K.order(s) # of index 2 in the maximal order of K
sage: L.<t> = K.extension(x^2 + 1)
sage: R = L.order((s, t))
sage: a = (1 + s)/2
sage: a.is_integral()
True
sage: L(a) in R # check that R does not contain the maximal order of K
False
}}}
Note the `L(a)` in the last line; this is because there is also the
following bug:
{{{
sage: s in R
False # clearly wrong because R = ZZ[s, t] as a subring of L
}}}
----
New commits:
||[http://git.sagemath.org/sage.git/commit/?id=987d39fce1db78d4085ed70688bd4733e0a721fb
987d39f]||{{{fix base ring of order in relative number field}}}||
||[http://git.sagemath.org/sage.git/commit/?id=2b459322c84d9dac7087eb30f1db4b73db6ccb8c
2b45932]||{{{fix base ring of orders in relative number fields}}}||
--
Ticket URL: <http://trac.sagemath.org/ticket/4738#comment:11>
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