#10174: relative norm in relative number fields is slow
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Reporter: thome | Owner: davidloeffler
Type: defect | Status: new
Priority: minor | Milestone:
Component: number fields | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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There seems to be no relative_norm or absolute_norm method for elements of
relative number fields (while there is for ideals). norm() works with an
optional base parameter, which can be set to the base field for obtaining
the relative norm.
However it's dog slow.
sage: K.<v>=NumberField(x^4 + 514*x^2 + 64321)
sage: L.<w>,e=K.galois_closure(map=True)
sage: R.<r,v>=L.relativize(e)
sage: time _=r.norm(K)
CPU times: user 0.44 s, sys: 0.00 s, total: 0.44 s
Wall time: 0.45 s
The attached patch changes the matrix() method to identify the base field
as a trivial case, so that r.norm(K) computes the relative norm quickly:
sage: K.<v>=NumberField(x^4 + 514*x^2 + 64321)
sage: L.<w>,e=K.galois_closure(map=True)
sage: R.<r,v>=L.relativize(e)
sage: time _=r.norm(K)
CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10174>
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