#8722: S-units sometimes broken and sometimes just plain wrong for relative
fields
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Reporter: davidloeffler | Owner: davidloeffler
Type: defect | Status: new
Priority: major | Milestone: sage-5.0
Component: number fields | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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{{{
sage: L.<a,b> = NumberField([x^2 + 1, x^2 - 5])
sage: p = L.ideal((-1/2*b - 1/2)*a + 1/2*b - 1/2)
sage: p.absolute_norm()
9
sage: p.is_prime()
True
sage: W = L.S_units([p]); W
[1/2*a + 7/4, a, 1/2*b - 1/2]
sage: W[0].valuation(L.primes_above(2)[0])
-4
}}}
So the first element of the list of S-units isn't actually an S-unit! In
other examples the code just blows up, because it calls
{{{residue_field}}} and that dies because of #8721:
{{{
sage: L.<a, b> = NumberField([polygen(QQ)^2 - 3, polygen(QQ)^2 - 5])
sage: L.S_units([L.ideal(a)])
}}}
This is arguably less bad: raising an error is far better than silently a
wrong answer.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8722>
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