Add construction method to function fields

[BrentBaccala]

This ticket enhances the function field code to add a construction functor and support the construction method:

sage: K.<x> = FunctionField(QQ)
sage: K.construction()
(FunctionField
 Fraction Field of Univariate Polynomial Ring in x over Rational Field)

sage: from sage.rings.function_field.function_field import FunctionFieldFunctor
sage: R.<x> = QQ[]
sage: FunctionFieldFunctor()(Frac(R))
Rational function field in x over Rational Field

Component: algebra

Keywords: function field

Author: Brent Baccala

Branch/Commit: public/27012 @ 62a8027

Issue created by migration from https://trac.sagemath.org/ticket/27012

[BrentBaccala]

Commit: 62a8027

[BrentBaccala]

Dependencies: #22982

[BrentBaccala]

New commits:

62a8027

Trac #27012: add construction method to FunctionField's

[BrentBaccala]

Author: Brent Baccala

[BrentBaccala]

Branch: public/27012

[BrentBaccala]

Changed dependencies from #22982 to none

[BrentBaccala]

comment:2

Don't think this needs 22892 as a dependency; it seems to commit fine with 8.5 as a base.

[BrentBaccala]

comment:4

I'm not sure where FunctionFieldFunctor should go. Right now, it's in function_field.py in the src/sage/rings/function_field directory.

Perhaps we should add a new file in that directory called functors.py? There's going to be at least one more ConstructionFunctor in the function field code, for constructing spaces of differentials.

[mezzarobba]

comment:5

While your patch looks sensible to me, that's not how things currently work for number fields. Instead, number fields are constructed directly from their base field by an AlgebraicConstructionFunctor. Can you explain why you are deviating from that model? (This may be a stupid question, I basically don't know anything about function fields.) And if your approach is better, should we use it from number fields too?

Also, you may want to add a couple of example of new coercions discovered thanks to the new construction, if there are any.

[BrentBaccala]

comment:6

Replying to @mezzarobba:

While your patch looks sensible to me, that's not how things currently work for number fields. Instead, number fields are constructed directly from their base field by an AlgebraicConstructionFunctor. Can you explain why you are deviating from that model? (This may be a stupid question, I basically don't know anything about function fields.) And if your approach is better, should we use it from number fields too?

I don't know if it's any better this way.

Also, you may want to add a couple of example of new coercions discovered thanks to the new construction, if there are any.

Well, the coercions I wanted it to discover, it couldn't, so I ended up coding them by hand (Trac #26993). I created this ticket because I didn't want to just throw this code away, but I don't know if it does anything useful.

[embray]

comment:7

Retarging tickets optimistically to the next milestone. If you are responsible for this ticket (either its reporter or owner) and don't believe you are likely to complete this ticket before the next release (8.7) please retarget this ticket's milestone to sage-pending or sage-wishlist.