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sage.rings.function_field: Update # needs #38732

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Oct 12, 2024
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sage.rings.function_field: Update # needs #38732

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9 changes: 9 additions & 0 deletions src/sage/rings/function_field/element.pyx
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Original file line number Diff line number Diff line change
Expand Up @@ -202,6 +202,7 @@ cdef class FunctionFieldElement(FieldElement):

We also substitute the generators in any base fields::

sage: # needs sage.rings.function_field
sage: K.<x> = FunctionField(QQ)
sage: R.<y> = K[]
sage: L.<y> = K.extension(y^3 - (x^3 + 2*x*y + 1/x))
Expand All @@ -224,6 +225,8 @@ cdef class FunctionFieldElement(FieldElement):
Traceback (most recent call last):
...
TypeError: in_dict must be a dict

sage: # needs sage.rings.function_field
sage: R.<y> = K[]
sage: L.<y> = K.extension(y^3 - (x^3 + 2*x*y + 1/x))
sage: f = x + y
Expand All @@ -234,6 +237,7 @@ cdef class FunctionFieldElement(FieldElement):

We can also substitute using dictionary syntax::

sage: # needs sage.rings.function_field
sage: K.<x> = FunctionField(QQ)
sage: R.<y> = K[]
sage: L.<y> = K.extension(y^3 - (x^3 + 2*x*y + 1/x))
Expand All @@ -249,6 +253,7 @@ cdef class FunctionFieldElement(FieldElement):

Check that we correctly handle extension fields::

sage: # needs sage.rings.function_field
sage: K.<x> = FunctionField(QQ)
sage: R.<y> = K[]
sage: L.<y> = K.extension(y^3 - (x^3 + 2*x*y + 1/x))
Expand All @@ -270,6 +275,7 @@ cdef class FunctionFieldElement(FieldElement):

Test that substitution works for rational functions::

sage: # needs sage.rings.function_field
sage: K.<x> = FunctionField(QQ)
sage: R.<y> = K[]
sage: L.<y> = K.extension(y^4 - 3)
Expand Down Expand Up @@ -298,6 +304,7 @@ cdef class FunctionFieldElement(FieldElement):

Same purpose as above but over an extension field over the rationals::

sage: # needs sage.rings.function_field
sage: K.<x> = FunctionField(QQ)
sage: R.<y> = K[]
sage: L.<y> = K.extension(y^3 - (x^3 + 2*x*y + 1/x))
Expand All @@ -319,6 +326,7 @@ cdef class FunctionFieldElement(FieldElement):

Test proper handling of not making substitutions::

sage: # needs sage.rings.function_field
sage: K.<x> = FunctionField(QQ)
sage: f = x
sage: f.subs() is f
Expand Down Expand Up @@ -357,6 +365,7 @@ cdef class FunctionFieldElement(FieldElement):

Test error handling with ambiguously named generators::

sage: # needs sage.rings.function_field
sage: K.<x> = FunctionField(QQ)
sage: R.<x> = K[]
sage: L.<x> = K.extension(x^3 - x)
Expand Down
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