Let number_field_elements_from_algebraics() return result using same field as input

[BrentBaccala]

I often want number_field_elements_from_algebraics() to return a morphism that goes back to the same field as the elements that I passed in.

For example:

sage: number_field_elements_from_algebraics(QQbar(2))
(Rational Field, 2, Ring morphism:
   From: Rational Field
   To:   Algebraic Real Field
   Defn: 1 |--> 1)

Notice that the morphism comes back to AA, not QQbar.

I've added an option to get the behavior that I want:

sage: number_field_elements_from_algebraics(QQbar(2), same_field=True)
(Rational Field, 2, Ring morphism:
   From: Rational Field
   To:   Algebraic Field
   Defn: 1 |--> 1)

Perhaps this should be the default, but it broke enough regression tests that I left it as an option.

Component: algebra

Author: Brent Baccala

Branch/Commit: ffa1e99

Reviewer: Marc Mezzarobba

Issue created by migration from https://trac.sagemath.org/ticket/25377

[BrentBaccala]

Branch: public/25377

[BrentBaccala]

New commits:

ffa1e99

Trac #25377: add 'same_field' option to number_field_elements_from_algebraics()

[BrentBaccala]

Author: Brent Baccala

[BrentBaccala]

Commit: ffa1e99

[videlec]

comment:2

I also think that this would better be the default. Where the failures are?

[videlec]

comment:3

Note: this ticket is likely to create conflicts #20181

[BrentBaccala]

comment:4

Replying to @videlec:

I also think that this would better be the default. Where the failures are?

This is the only troublesome one:

sage: a = QQbar((-1)^(1/4)); b = AA(a^3-a); t = b.as_number_field_element()

It raises an exception with the new code (if same_field=True is the default).

The problem is that without minimal=True, the generated number field might be complex, and thus unable to map back to AA.

So, if the elements are from AA, same_field=True might not work without minimal=True, and I wasn't inclined to change that default.

[mezzarobba]

Reviewer: Marc Mezzarobba

[mezzarobba]

comment:5

Replying to @BrentBaccala:

The problem is that without minimal=True, the generated number field might be complex, and thus unable to map back to AA.

So, if the elements are from AA, same_field=True might not work without minimal=True, and I wasn't inclined to change that default.

Sounds sensible. And the code looks good to me. One minor nitpick (not worth delaying the ticket IMO): I personally don't like the use of _ to store a value that you are going to access again (as opposed to cases like a, _, b = foo where you need to provide a variable but don't care about the value).

[vbraun]

Changed branch from public/25377 to ffa1e99