make composite_fields and galois_closure return maps and preserve embeddings

[93749b3a-c0a4-47a7-b178-004ba08b0b97]

The patches describe and doctest this better, but...

• Extends composite_fields and galois_closure to return maps when asked

• Uses the new coercion embedding to only return "coherent" compositions if embeddings are specified.

Component: number theory

Keywords: number fields composite fields galois closure embedding coercion

Issue created by migration from https://trac.sagemath.org/ticket/5228

[93749b3a-c0a4-47a7-b178-004ba08b0b97]

Attachment: trac_5228-composite-fields.patch.gz

[93749b3a-c0a4-47a7-b178-004ba08b0b97]

comment:1

Attachment: trac_5228-composite-fields-embeddings.patch.gz

Apply trac_5228-composite-fields.patch and then trac_5228-composite-fields-embeddings.patch

[85eec1a4-3d04-4b4d-b711-d4db03337c41]

comment:2

Assign it to 3.4.1 for now. If it is reviewed in time and passes doctests it will go into 3.3.

Cheers,

Michael

[aghitza]

comment:3

Since someone beat me to #5231, I had to review this one...

Looks good.

[85eec1a4-3d04-4b4d-b711-d4db03337c41]

comment:4

Merged both patches in Sage 3.3.rc1.

Cheers,

Michael