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gh-35957: `sage.rings.function_field`: Update `# needs` <!-- ^^^^^ Please provide a concise, informative and self-explanatory title. Don't put issue numbers in there, do this in the PR body below. For example, instead of "Fixes #1234" use "Introduce new method to calculate 1+1" --> <!-- Describe your changes here in detail --> - 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 <!-- Why is this change required? What problem does it solve? --> <!-- If this PR resolves an open issue, please link to it here. For example "Fixes #12345". --> This is: - done with the help of `sage -fixdoctests` from #35749 - Part of: #29705 - Cherry-picked from: #35095 ### 📝 Checklist <!-- Put an `x` in all the boxes that apply. --> <!-- If your change requires a documentation PR, please link it appropriately --> <!-- If you're unsure about any of these, don't hesitate to ask. We're here to help! --> <!-- Feel free to remove irrelevant items. --> - [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 <!-- List all open PRs that this PR logically depends on - #12345: short description why this is a dependency - #34567: ... --> <!-- If you're unsure about any of these, don't hesitate to ask. We're here to help! --> URL: #35957 Reported by: Matthias Köppe Reviewer(s): David Coudert, Matthias Köppe
2 parents ce5b249 + 61654eb commit 448341b

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‎src/sage/rings/function_field/constructor.py

Lines changed: 18 additions & 18 deletions
Original file line numberDiff line numberDiff line change
@@ -57,10 +57,10 @@ class FunctionFieldFactory(UniqueFactory):
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sage: K.<x> = FunctionField(QQ); K
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Rational function field in x over Rational Field
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sage: L.<y> = FunctionField(GF(7)); L # optional - sage.rings.finite_rings
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sage: L.<y> = FunctionField(GF(7)); L
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Rational function field in y over Finite Field of size 7
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sage: R.<z> = L[] # optional - sage.rings.finite_rings
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sage: M.<z> = L.extension(z^7 - z - y); M # optional - sage.rings.finite_rings sage.rings.function_field
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sage: R.<z> = L[]
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sage: M.<z> = L.extension(z^7 - z - y); M # needs sage.rings.finite_rings sage.rings.function_field
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Function field in z defined by z^7 + 6*z + 6*y
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TESTS::
@@ -69,8 +69,8 @@ class FunctionFieldFactory(UniqueFactory):
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sage: L.<x> = FunctionField(QQ)
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sage: K is L
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True
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sage: M.<x> = FunctionField(GF(7)) # optional - sage.rings.finite_rings
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sage: K is M # optional - sage.rings.finite_rings
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sage: M.<x> = FunctionField(GF(7))
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sage: K is M
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False
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sage: N.<y> = FunctionField(QQ)
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sage: K is N
@@ -136,9 +136,9 @@ class FunctionFieldExtensionFactory(UniqueFactory):
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sage: y2 = y*1
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sage: y2 is y
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False
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sage: L.<w> = K.extension(x - y^2) # optional - sage.rings.function_field
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sage: M.<w> = K.extension(x - y2^2) # optional - sage.rings.function_field
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sage: L is M # optional - sage.rings.function_field
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sage: L.<w> = K.extension(x - y^2) # needs sage.rings.function_field
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sage: M.<w> = K.extension(x - y2^2) # needs sage.rings.function_field
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sage: L is M # needs sage.rings.function_field
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True
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"""
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def create_key(self,polynomial,names):
@@ -150,20 +150,20 @@ def create_key(self,polynomial,names):
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sage: K.<x> = FunctionField(QQ)
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sage: R.<y> = K[]
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sage: L.<w> = K.extension(x - y^2) # indirect doctest # optional - sage.rings.function_field
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sage: L.<w> = K.extension(x - y^2) # indirect doctest # needs sage.rings.function_field
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TESTS:
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Verify that :trac:`16530` has been resolved::
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sage: K.<x> = FunctionField(QQ)
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sage: R.<y> = K[]
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sage: L.<y> = K.extension(y^2 - x) # optional - sage.rings.function_field
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sage: R.<z> = L[] # optional - sage.rings.function_field
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sage: M.<z> = L.extension(z - 1) # optional - sage.rings.function_field
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sage: L.<y> = K.extension(y^2 - x) # needs sage.rings.function_field
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sage: R.<z> = L[] # needs sage.rings.function_field
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sage: M.<z> = L.extension(z - 1) # needs sage.rings.function_field
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sage: R.<z> = K[]
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sage: N.<z> = K.extension(z - 1) # optional - sage.rings.function_field
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sage: M is N # optional - sage.rings.function_field
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sage: N.<z> = K.extension(z - 1) # needs sage.rings.function_field
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sage: M is N # needs sage.rings.function_field
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False
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"""
@@ -182,10 +182,10 @@ def create_object(self,version,key,**extra_args):
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sage: K.<x> = FunctionField(QQ)
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sage: R.<y> = K[]
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sage: L.<w> = K.extension(x - y^2) # indirect doctest # optional - sage.rings.function_field
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sage: y2 = y*1 # optional - sage.rings.function_field
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sage: M.<w> = K.extension(x - y2^2) # indirect doctest # optional - sage.rings.function_field
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sage: L is M # optional - sage.rings.function_field
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sage: L.<w> = K.extension(x - y^2) # indirect doctest # needs sage.rings.function_field
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sage: y2 = y*1
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sage: M.<w> = K.extension(x - y2^2) # indirect doctest # needs sage.rings.function_field
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sage: L is M # needs sage.rings.function_field
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True
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"""
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from . import function_field_polymod, function_field_rational

‎src/sage/rings/function_field/derivations.py

Lines changed: 4 additions & 4 deletions
Original file line numberDiff line numberDiff line change
@@ -4,10 +4,10 @@
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For global function fields, which have positive characteristics, the higher
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derivation is available::
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7-
sage: K.<x> = FunctionField(GF(2)); _.<Y> = K[] # optional - sage.rings.finite_rings
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sage: L.<y> = K.extension(Y^3 + x + x^3*Y) # optional - sage.rings.finite_rings sage.rings.function_field
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sage: h = L.higher_derivation() # optional - sage.rings.finite_rings sage.rings.function_field
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sage: h(y^2, 2) # optional - sage.rings.finite_rings sage.rings.function_field
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sage: K.<x> = FunctionField(GF(2)); _.<Y> = K[]
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sage: L.<y> = K.extension(Y^3 + x + x^3*Y) # needs sage.rings.function_field
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sage: h = L.higher_derivation() # needs sage.rings.function_field
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sage: h(y^2, 2) # needs sage.rings.function_field
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((x^7 + 1)/x^2)*y^2 + x^3*y
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