abs for elements of number fields provided with a complex embedding ignores it

[sagetrac-fwclarke]

See http://ask.sagemath.org/question/3967/qqextension-with-embedding-incorrect-modulus

sage: x = polygen(ZZ)
sage: f = x^3 - x - 1
sage: beta = f.complex_roots()[0]; beta
1.32471795724475
sage: K.<b> = NumberField(f, embedding=beta)
sage: b.abs()
0.868836961832709
sage: [r.abs() for r in f.complex_roots()]
[1.32471795724475, 0.868836961832709, 0.868836961832709]

Component: number fields

Author: Vincent Delecroix

Branch/Commit: 56042dc

Reviewer: Francis Clarke

Issue created by migration from https://trac.sagemath.org/ticket/16147

[videlec]

comment:2

I provided a simple fix... needs review!

Vincent

---

New commits:

56042dc

trac #16147: fix .abs() for elt of embedded number field

[videlec]

Branch: u/vdelecroix/16147

[videlec]

Author: Vincent Delecroix

[videlec]

Commit: 56042dc

[sagetrac-fwclarke]

comment:3

Does the job very neatly: positive review.

[videlec]

Reviewer: Francis Clarke

[videlec]

comment:4

Replying to @sagetrac-fwclarke:

Does the job very neatly: positive review.

Great! thanks!

When you finish the review, you might better fill the reviewer field with your name (otherwise the release manager has extra job to do). It should be filled with your full name. I did it for you anyway.

Vincent

PS: Actually, I thought that the default answer of .abs() could be an element of QQbar (whenever an embedding in QQbar is defined). That way we would have an exact algebraic number and not an approximation. But in order to do that, there is something to fix with embeddings:

sage: K.<cbrt2> = NumberField(x^3 - 2, embedding=1)
sage: QQbar.has_coerce_map_from(K)
False

[vbraun]

Changed branch from u/vdelecroix/16147 to 56042dc