Better isomorphisms between function fields and fraction fields

[saraedum]

Add a method function_field to fraction fields of univariate polynomial rings over fields which returns the isomorphic function field. Also, the involved morphisms should know that they are injective and surjective.

Component: commutative algebra

Keywords: function field, fraction field

Author: Julian Rüth

Branch: 746eac0

Reviewer: Jean-Pierre Flori

Issue created by migration from https://trac.sagemath.org/ticket/23660

[saraedum]

Branch: u/saraedum/better_isomorphisms_between_function_fields_and_fraction_fields

[saraedum]

New commits:

f6dd0cd

Better isomorphisms between fraction fields and function fields

[saraedum]

Commit: f6dd0cd

[jpflori]

Reviewer: Jean-Pierre Flori

[jpflori]

comment:3

Looks fine.

Maybe you could make the paragraph in _richcmp_ a warning or note block.

[saraedum]

comment:4

done.

[sagetrac-git]

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

38f18b8

minor docstring change

[sagetrac-git]

Changed commit from f6dd0cd to 38f18b8

[vbraun]

comment:7

File "src/sage/categories/rings.py", line 117, in sage.categories.rings.Rings.MorphismMethods.is_injective
Failed example:
    f = ZZ.hom(K); f
Expected:
    Composite map:
      From: Integer Ring
      To:   Rational function field in x over Rational Field
      Defn:   Conversion via FractionFieldElement_1poly_field map:
              From: Integer Ring
              To:   Fraction Field of Univariate Polynomial Ring in x over Rational Field
            then
              Coercion map:
              From: Fraction Field of Univariate Polynomial Ring in x over Rational Field
              To:   Rational function field in x over Rational Field
Got:
    Composite map:
      From: Integer Ring
      To:   Rational function field in x over Rational Field
      Defn:   Conversion via FractionFieldElement_1poly_field map:
              From: Integer Ring
              To:   Fraction Field of Univariate Polynomial Ring in x over Rational Field
            then
              Isomorphism morphism:
              From: Fraction Field of Univariate Polynomial Ring in x over Rational Field
              To:   Rational function field in x over Rational Field

[sagetrac-git]

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

8bfe326

Merge branch 'develop' into t/23660/better_isomorphisms_between_function_fields_and_fraction_fields

[sagetrac-git]

Changed commit from 38f18b8 to 8bfe326

[sagetrac-git]

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

746eac0

fix docstring

[sagetrac-git]

Changed commit from 8bfe326 to 746eac0

[saraedum]

Work Issues: patchbot happy⇒back to positive review

[roed314]

Changed work issues from patchbot happy⇒back to positive review to none

[roed314]

comment:11

Patchbot's happy.

[vbraun]

Changed branch from u/saraedum/better_isomorphisms_between_function_fields_and_fraction_fields to 746eac0

[jdemeyer]

comment:13

This broke #23881 :-(

[jdemeyer]

Changed commit from 746eac0 to none

[jdemeyer]

comment:14

Follow-up: #24033