From 74deb42f37297af89a58f1e20b9ac32624a95e3b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Rub=C3=A9n=20Mu=C3=B1oz--Bertrand?=
 <ruben.munoz-bertrand@inria.fr>
Date: Wed, 22 Oct 2025 19:46:33 +0200
Subject: [PATCH] Fix bug with creation of extensions of function fields

---
 .../rings/function_field/function_field.py    | 15 ++++++++-
 .../function_field/function_field_rational.py | 32 -------------------
 2 files changed, 14 insertions(+), 33 deletions(-)

diff --git a/src/sage/rings/function_field/function_field.py b/src/sage/rings/function_field/function_field.py
index 2e2ece950ad..347c24a9ab8 100644
--- a/src/sage/rings/function_field/function_field.py
+++ b/src/sage/rings/function_field/function_field.py
@@ -467,9 +467,22 @@ def extension(self, f, names=None):
 
             sage: K.extension(t*y^3 + (1/t)*y + t^3/(t+1))                              # needs sage.rings.function_field
             Function field in y defined by t*y^3 + 1/t*y + t^3/(t + 1)
+
+        TESTS:
+
+        Verify that :issue:`41095` has been resolved::
+
+            sage: K.<x> = FunctionField(GF(2))
+            sage: R.<t> = PolynomialRing(K)
+            sage: L.<y> = K.extension(t^2 + t*x)
+            sage: M.<z> = L.extension(t^3 + x)
+            sage: M.base_ring() is K
+            False
+            sage: M.base_ring() is L
+            True
         """
         from . import constructor
-        return constructor.FunctionFieldExtension(f, names)
+        return constructor.FunctionFieldExtension(f.change_ring(self), names)
 
     def order_with_basis(self, basis, check: bool = True):
         """
diff --git a/src/sage/rings/function_field/function_field_rational.py b/src/sage/rings/function_field/function_field_rational.py
index ffc72b51f33..c9b4a9042d9 100644
--- a/src/sage/rings/function_field/function_field_rational.py
+++ b/src/sage/rings/function_field/function_field_rational.py
@@ -430,38 +430,6 @@ def _factor_univariate_polynomial(self, f, proof=None):
         from sage.structure.factorization import Factorization
         return Factorization(w, unit=unit)
 
-    def extension(self, f, names=None):
-        """
-        Create an extension `L = K[y]/(f(y))` of the rational function field.
-
-        INPUT:
-
-        - ``f`` -- univariate polynomial over self
-
-        - ``names`` -- string or length-1 tuple
-
-        OUTPUT: a function field
-
-        EXAMPLES::
-
-            sage: K.<x> = FunctionField(QQ); R.<y> = K[]
-            sage: K.extension(y^5 - x^3 - 3*x + x*y)                                    # needs sage.rings.function_field
-            Function field in y defined by y^5 + x*y - x^3 - 3*x
-
-        A nonintegral defining polynomial::
-
-            sage: K.<t> = FunctionField(QQ); R.<y> = K[]
-            sage: K.extension(y^3 + (1/t)*y + t^3/(t+1))                                # needs sage.rings.function_field
-            Function field in y defined by y^3 + 1/t*y + t^3/(t + 1)
-
-        The defining polynomial need not be monic or integral::
-
-            sage: K.extension(t*y^3 + (1/t)*y + t^3/(t+1))                              # needs sage.rings.function_field
-            Function field in y defined by t*y^3 + 1/t*y + t^3/(t + 1)
-        """
-        from . import constructor
-        return constructor.FunctionFieldExtension(f, names)
-
     @cached_method
     def polynomial_ring(self, var='x'):
         """