#8722 closed defect (fixed)
S-units sometimes broken and sometimes just plain wrong for relative fields
Reported by: | davidloeffler | Owned by: | davidloeffler |
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Priority: | major | Milestone: | sage-4.4 |
Component: | number fields | Keywords: | |
Cc: | Merged in: | sage-4.4.alpha2 | |
Authors: | David Loeffler | Reviewers: | John Cremona |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
The code for S-unit groups of number fields calls the degree
method. For relative number fields this deliberately returns an error, because of the ambiguity between absolute and relative degree.
sage: L.<a,b> = NumberField([x^2 + 1, x^2 - 5]) sage: sage: p = L.ideal((-1/2*b - 1/2)*a + 1/2*b - 1/2) sage: sage: W = L.S_units([p]); W --------------------------------------------------------------------------- NotImplementedError Traceback (most recent call last) ... NotImplementedError: For a relative number field you must use relative_degree or absolute_degree as appropriate
In this case I think it should be absolute_degree, but changing this returns wrong output:
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.
Attachments (1)
Change History (6)
comment:1 Changed 10 years ago by
- Description modified (diff)
comment:2 Changed 10 years ago by
- Status changed from new to needs_review
comment:3 Changed 10 years ago by
- Status changed from needs_review to positive_review
Looks good, applied fine to 4.4.alpha0 + #8446 patches, and all tests in sage/rings/number_field pass.
Positive review!
comment:4 Changed 10 years ago by
- Merged in set to sage-4.4.alpha2
- Resolution set to fixed
- Reviewers set to John Cremona
- Status changed from positive_review to closed
Merged into 4.4.alpha2.
comment:5 Changed 10 years ago by
- Milestone changed from sage-5.0 to sage-4.4
Here's a patch. Turns out that the code was using
K.gen
and the correct answer is to callK.absolute_generator
, which isn't the same in the above example. This fixes the first example; the second is an instance of #8721.