Make subfield methods compatible, implement for more fields

[mkoeppe]

For finite fields, #27949 added a subfield method.

Absolute number fields have a subfield method, but it is incompatible with the one added for finite fields.

sage: K.<sqrt2> = QuadraticField(2)
sage: K.subfield(1)
(Number Field in sqrt20 with defining polynomial x - 1 with sqrt20 = 1,
 Ring morphism:
   From: Number Field in sqrt20 with defining polynomial x - 1 with sqrt20 = 1
   To:   Number Field in sqrt2 with defining polynomial x^2 - 2 with sqrt2 = 1.414213562373095?
   Defn: 1 |--> 1)

#23245 notes that RationalField lacks many methods of general number fields, include subfield

See also: #14956, #6092

CC: @kliem @videlec @kwankyu @tscrim @fchapoton

Component: algebra

Issue created by migration from https://trac.sagemath.org/ticket/30171

[kwankyu]

comment:2

Assuming that we want them compatible, I am leaning to the version of the finite fields subfield() methods, where the ring morphism is not returned as a coercion map is available indirectly. But heavy users of number fields might have different opinions.

[mkoeppe]

comment:3

A way to make them compatible would be to have an option return_map.

[kwankyu]

comment:4

Replying to @mkoeppe:

A way to make them compatible would be to have an option return_map.

More common name for the option is probably map=True.

[mkoeppe]

comment:5

Sounds good

[mkoeppe]

comment:7

Sage development has entered the release candidate phase for 9.3. Setting a new milestone for this ticket based on a cursory review of ticket status, priority, and last modification date.