#7703: S-units, S-class groups, and selmer groups of etale algebras
-----------------------------+----------------------------------------------
Reporter: rlm | Owner: was
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.3.1
Component: number theory | Keywords: number fields selmer groups
Work_issues: | Author: Robert Miller
Upstream: N/A | Reviewer: John Cremona
Merged: |
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Changes (by cremona):
* keywords: => number fields selmer groups
* reviewer: => John Cremona
* status: needs_review => needs_work
Comment:
As soon as I tried out an example of my own I hit a problem -- the
functions S_class_group(), S_unit_group() and selmer_group() only apply to
objects of type
'sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_field'
and not to number fields! The first thing I wanted to do was
{{{
sage: K.<a> = QuadraticField(-23)
sage: K.selmer_group([],3)
}}}
and that does not work, you have to form the polynomial ring K[] and then
quotient out the generator x to get something isomorphic to K which has
forgotten that it is a number field.
Can we not design things so that number fields are a special case of etale
algebras in a slightly more transparent way? Failing that, can we not
implement the three functions just mentioned for number fields directly?
This is what I would need!
If that would be easy, I suggest adding it right now before merging this
in. But if there are difficulties, I could be persuaded to get this in
now as it is as long as there was a clear TODO and a new ticket to do what
I want.
I have therefore tagged the ticket as "needs work", but you (rlm) should
feel free to argue for the second option, put it back to "needs review"
and (if I am convinced by the argument ;)) will come back to give it a
positive review.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7703#comment:13>
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