#7643: composite_fields does not play nice with QuadraticFields
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Reporter: rlm | Owner: davidloeffler
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.3.1
Component: number fields | Keywords:
Work_issues: | Author: Francis Clarke
Upstream: N/A | Reviewer: John Cremona
Merged: |
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Changes (by fwclarke):
* status: needs_info => needs_review
Comment:
Replying to [comment:2 cremona]:
> Quick question: in cases where we compute K.composite_fields(L) where
there is an embedding of K into L or K into K, would it not be nice to
return L (resp K) rather than some new field? Surely that would not be
expensive to test for.
This is an excellent idea. In principle it's easy to implement, because
we only have to see if the degrees are equal. In practice it all becomes
quite complicated when embeddings, maps and relative fields are taken into
account, and I fear the the code in the replacement patch which I attach
is even more convoluted than before.
One of the complications was that I needed to obtain the inverse of an
isomorphism between distinct fields. At present one can only take the
inverse of an ''automorphism'' of a field. So the patch includes some
minor tweaks to `rings/number_field/morphism.py`, `categories/map.pyx` and
`modules/matrix_morphism.py` in order to do this neatly. In particular,
after the patch one can raise a map to the power -1, when the inverse is
defined.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7643#comment:3>
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