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Matthias Koeppe
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./sage -fixdoctests --distribution sagemath-categories --probe all --only-tags src/sage/rings/function_field
1 parent 9f672a2 commit 74641bb

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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: 5 additions & 4 deletions
Original file line numberDiff line numberDiff line change
@@ -4,10 +4,11 @@
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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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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: # needs sage.rings.finite_rings
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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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