residue field of a valuation on a function field should be a function field when possible

[saraedum]

Currently, the residue field of a non-classical valuation on a function field is not a real function field:

sage: R.<x> = QQ[]
sage: v = GaussValuation(R, QQ.valuation(2))
sage: K.<x> = FunctionField(QQ)
sage: v = K.valuation(v)
sage: v.residue_field()
Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 2 (using GF2X)

This ticket changes this to be Rational function field in x over Finite Field of size 2.

CC: @sagetrac-swewers

Component: commutative algebra

Author: Julian Rüth

Branch/Commit: 34a2d19

Reviewer: Stefan Wewers

Issue created by migration from https://trac.sagemath.org/ticket/26123

[saraedum]

Work Issues: is the patchbot happy?

[saraedum]

Branch: u/saraedum/26123

[sagetrac-swewers]

Commit: a5c8755

[sagetrac-swewers]

comment:4

There should be a test that v.reduce(f) works in this situation.
The docstring for reduce test this only for standard valuations,
where the residue field is not a function field.

---

New commits:

a5c8755

Make residue_ring of a valuation on a function field a function field

[saraedum]

comment:5

We have _test_reduce in valuation_space.py that tests generically that v.reduce(f) is in v.residue_ring(). So let's add a check there that v.residue_ring() coerces into v.residue_field().

[saraedum]

comment:6

Hm…so since residue_ring() and residue_field() are the same in this case, I don't think we need this here ;)

[saraedum]

Changed work issues from is the patchbot happy? to is the patchbot happy? no.

[sagetrac-git]

Changed commit from a5c8755 to 09e076f

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

5bb3a1f	Merge remote-tracking branch 'trac/develop' into 26123
09e076f	Fix residue_ring() for pseudo-valuations on function fields

[saraedum]

New commits:

5bb3a1f	Merge remote-tracking branch 'trac/develop' into 26123
09e076f	Fix residue_ring() for pseudo-valuations on function fields

[saraedum]

Changed work issues from is the patchbot happy? no. to is the patchbot happy?

[sagetrac-swewers]

comment:10

Trivial pyflakes error:

src/sage/rings/valuation/valuation_space.py:1563: local variable 'r' is assigned to but never used

Otherwise, everything is fine.

[sagetrac-swewers]

Reviewer: Stefan Wewers

[sagetrac-swewers]

Changed work issues from is the patchbot happy? to is the patchbot happy? no

[sagetrac-git]

Changed commit from 09e076f to 34a2d19

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

274f2e0	fix pyflakes warning
34a2d19	Fix doctest output in documentation

[saraedum]

Changed work issues from is the patchbot happy? no to is the patchbot happy?

[sagetrac-swewers]

Changed work issues from is the patchbot happy? to none

[vbraun]

Changed branch from u/saraedum/26123 to 34a2d19