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gh-35957: sage.rings.function_field: Update # needs
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- Many `# optional` are removed because small prime finite fields no
longer need to be marked `# optional/needs sage.rings.finite_rings`
since #35847
- Other `# optional` are replaced by codeblock-scoped `# needs` tags
- Remaining `# optional` with standard features are replaced by `#
needs`
- Some import fixes needed for separate testing of **sagemath-graphs**
from #35095
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This is:
- done with the help of `sage -fixdoctests` from #35749
- Part of: #29705
- Cherry-picked from: #35095

### 📝 Checklist

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- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
- [x] I have linked a relevant issue or discussion.
- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation accordingly.

### ⌛ Dependencies

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URL: #35957
Reported by: Matthias Köppe
Reviewer(s): David Coudert, Matthias Köppe
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Release Manager committed Jul 29, 2023
2 parents ce5b249 + 61654eb commit 448341b
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Showing 23 changed files with 2,638 additions and 2,350 deletions.
36 changes: 18 additions & 18 deletions src/sage/rings/function_field/constructor.py
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Original file line number Diff line number Diff line change
Expand Up @@ -57,10 +57,10 @@ class FunctionFieldFactory(UniqueFactory):
sage: K.<x> = FunctionField(QQ); K
Rational function field in x over Rational Field
sage: L.<y> = FunctionField(GF(7)); L # optional - sage.rings.finite_rings
sage: L.<y> = FunctionField(GF(7)); L
Rational function field in y over Finite Field of size 7
sage: R.<z> = L[] # optional - sage.rings.finite_rings
sage: M.<z> = L.extension(z^7 - z - y); M # optional - sage.rings.finite_rings sage.rings.function_field
sage: R.<z> = L[]
sage: M.<z> = L.extension(z^7 - z - y); M # needs sage.rings.finite_rings sage.rings.function_field
Function field in z defined by z^7 + 6*z + 6*y
TESTS::
Expand All @@ -69,8 +69,8 @@ class FunctionFieldFactory(UniqueFactory):
sage: L.<x> = FunctionField(QQ)
sage: K is L
True
sage: M.<x> = FunctionField(GF(7)) # optional - sage.rings.finite_rings
sage: K is M # optional - sage.rings.finite_rings
sage: M.<x> = FunctionField(GF(7))
sage: K is M
False
sage: N.<y> = FunctionField(QQ)
sage: K is N
Expand Down Expand Up @@ -136,9 +136,9 @@ class FunctionFieldExtensionFactory(UniqueFactory):
sage: y2 = y*1
sage: y2 is y
False
sage: L.<w> = K.extension(x - y^2) # optional - sage.rings.function_field
sage: M.<w> = K.extension(x - y2^2) # optional - sage.rings.function_field
sage: L is M # optional - sage.rings.function_field
sage: L.<w> = K.extension(x - y^2) # needs sage.rings.function_field
sage: M.<w> = K.extension(x - y2^2) # needs sage.rings.function_field
sage: L is M # needs sage.rings.function_field
True
"""
def create_key(self,polynomial,names):
Expand All @@ -150,20 +150,20 @@ def create_key(self,polynomial,names):
sage: K.<x> = FunctionField(QQ)
sage: R.<y> = K[]
sage: L.<w> = K.extension(x - y^2) # indirect doctest # optional - sage.rings.function_field
sage: L.<w> = K.extension(x - y^2) # indirect doctest # needs sage.rings.function_field
TESTS:
Verify that :trac:`16530` has been resolved::
sage: K.<x> = FunctionField(QQ)
sage: R.<y> = K[]
sage: L.<y> = K.extension(y^2 - x) # optional - sage.rings.function_field
sage: R.<z> = L[] # optional - sage.rings.function_field
sage: M.<z> = L.extension(z - 1) # optional - sage.rings.function_field
sage: L.<y> = K.extension(y^2 - x) # needs sage.rings.function_field
sage: R.<z> = L[] # needs sage.rings.function_field
sage: M.<z> = L.extension(z - 1) # needs sage.rings.function_field
sage: R.<z> = K[]
sage: N.<z> = K.extension(z - 1) # optional - sage.rings.function_field
sage: M is N # optional - sage.rings.function_field
sage: N.<z> = K.extension(z - 1) # needs sage.rings.function_field
sage: M is N # needs sage.rings.function_field
False
"""
Expand All @@ -182,10 +182,10 @@ def create_object(self,version,key,**extra_args):
sage: K.<x> = FunctionField(QQ)
sage: R.<y> = K[]
sage: L.<w> = K.extension(x - y^2) # indirect doctest # optional - sage.rings.function_field
sage: y2 = y*1 # optional - sage.rings.function_field
sage: M.<w> = K.extension(x - y2^2) # indirect doctest # optional - sage.rings.function_field
sage: L is M # optional - sage.rings.function_field
sage: L.<w> = K.extension(x - y^2) # indirect doctest # needs sage.rings.function_field
sage: y2 = y*1
sage: M.<w> = K.extension(x - y2^2) # indirect doctest # needs sage.rings.function_field
sage: L is M # needs sage.rings.function_field
True
"""
from . import function_field_polymod, function_field_rational
Expand Down
8 changes: 4 additions & 4 deletions src/sage/rings/function_field/derivations.py
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Original file line number Diff line number Diff line change
Expand Up @@ -4,10 +4,10 @@
For global function fields, which have positive characteristics, the higher
derivation is available::
sage: K.<x> = FunctionField(GF(2)); _.<Y> = K[] # optional - sage.rings.finite_rings
sage: L.<y> = K.extension(Y^3 + x + x^3*Y) # optional - sage.rings.finite_rings sage.rings.function_field
sage: h = L.higher_derivation() # optional - sage.rings.finite_rings sage.rings.function_field
sage: h(y^2, 2) # optional - sage.rings.finite_rings sage.rings.function_field
sage: K.<x> = FunctionField(GF(2)); _.<Y> = K[]
sage: L.<y> = K.extension(Y^3 + x + x^3*Y) # needs sage.rings.function_field
sage: h = L.higher_derivation() # needs sage.rings.function_field
sage: h(y^2, 2) # needs sage.rings.function_field
((x^7 + 1)/x^2)*y^2 + x^3*y
AUTHORS:
Expand Down
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