diff --git a/src/sage/rings/function_field/differential.py b/src/sage/rings/function_field/differential.py
index ba2144d910b..4442a63bd22 100644
--- a/src/sage/rings/function_field/differential.py
+++ b/src/sage/rings/function_field/differential.py
@@ -1,4 +1,4 @@
-# sage.doctest: optional - sage.modules
+# sage.doctest: needs sage.modules
 """
 Differentials of function fields
 
diff --git a/src/sage/rings/function_field/divisor.py b/src/sage/rings/function_field/divisor.py
index f3dddb48d7c..30d99d920d4 100644
--- a/src/sage/rings/function_field/divisor.py
+++ b/src/sage/rings/function_field/divisor.py
@@ -1,5 +1,5 @@
-# sage.doctest: optional - sage.rings.finite_rings               (because all doctests use finite fields)
-# sage.doctest: optional - sage.rings.function_field    (because almost all doctests use function field extensions)
+# sage.doctest: needs sage.rings.finite_rings               (because all doctests use finite fields)
+# sage.doctest: needs sage.rings.function_field    (because almost all doctests use function field extensions)
 """
 Divisors of function fields
 
diff --git a/src/sage/rings/function_field/drinfeld_modules/action.py b/src/sage/rings/function_field/drinfeld_modules/action.py
index cfa9774058a..6fca6225d60 100644
--- a/src/sage/rings/function_field/drinfeld_modules/action.py
+++ b/src/sage/rings/function_field/drinfeld_modules/action.py
@@ -1,4 +1,4 @@
-# sage.doctest: optional - sage.rings.finite_rings
+# sage.doctest: needs sage.rings.finite_rings
 r"""
 The module action induced by a Drinfeld module
 
diff --git a/src/sage/rings/function_field/drinfeld_modules/drinfeld_module.py b/src/sage/rings/function_field/drinfeld_modules/drinfeld_module.py
index 958347113c0..55b4cfab326 100644
--- a/src/sage/rings/function_field/drinfeld_modules/drinfeld_module.py
+++ b/src/sage/rings/function_field/drinfeld_modules/drinfeld_module.py
@@ -1,4 +1,4 @@
-# sage.doctest: optional - sage.rings.finite_rings
+# sage.doctest: needs sage.rings.finite_rings
 r"""
 Drinfeld modules
 
diff --git a/src/sage/rings/function_field/drinfeld_modules/finite_drinfeld_module.py b/src/sage/rings/function_field/drinfeld_modules/finite_drinfeld_module.py
index 5c834733321..470dfc495d7 100644
--- a/src/sage/rings/function_field/drinfeld_modules/finite_drinfeld_module.py
+++ b/src/sage/rings/function_field/drinfeld_modules/finite_drinfeld_module.py
@@ -1,4 +1,4 @@
-# sage.doctest: optional - sage.rings.finite_rings
+# sage.doctest: needs sage.rings.finite_rings
 r"""
 Finite Drinfeld modules
 
diff --git a/src/sage/rings/function_field/drinfeld_modules/homset.py b/src/sage/rings/function_field/drinfeld_modules/homset.py
index 9ca53442cf5..d50e943686b 100644
--- a/src/sage/rings/function_field/drinfeld_modules/homset.py
+++ b/src/sage/rings/function_field/drinfeld_modules/homset.py
@@ -1,4 +1,4 @@
-# sage.doctest: optional - sage.rings.finite_rings
+# sage.doctest: needs sage.rings.finite_rings
 r"""
 Set of morphisms between two Drinfeld modules
 
diff --git a/src/sage/rings/function_field/drinfeld_modules/morphism.py b/src/sage/rings/function_field/drinfeld_modules/morphism.py
index dfed15f778c..c7e1f6c3bfe 100644
--- a/src/sage/rings/function_field/drinfeld_modules/morphism.py
+++ b/src/sage/rings/function_field/drinfeld_modules/morphism.py
@@ -1,4 +1,4 @@
-# sage.doctest: optional - sage.rings.finite_rings
+# sage.doctest: needs sage.rings.finite_rings
 r"""
 Drinfeld module morphisms
 
diff --git a/src/sage/rings/function_field/element.pyx b/src/sage/rings/function_field/element.pyx
index a5699080814..5e8254e8294 100644
--- a/src/sage/rings/function_field/element.pyx
+++ b/src/sage/rings/function_field/element.pyx
@@ -187,7 +187,7 @@ cdef class FunctionFieldElement(FieldElement):
 
         Now an example in a nontrivial extension of a rational function field::
 
-            sage: # needs sage.modules sage.rings.function_field
+            sage: # needs sage.rings.function_field
             sage: K.<x> = FunctionField(QQ); R.<y> = K[]
             sage: L.<y> = K.extension(y^2 - x*y + 4*x^3)
             sage: y.matrix()
@@ -199,7 +199,7 @@ cdef class FunctionFieldElement(FieldElement):
         An example in a relative extension, where neither function
         field is rational::
 
-            sage: # needs sage.modules sage.rings.function_field
+            sage: # needs sage.rings.function_field
             sage: K.<x> = FunctionField(QQ)
             sage: R.<y> = K[]
             sage: L.<y> = K.extension(y^2 - x*y + 4*x^3)
@@ -222,7 +222,7 @@ cdef class FunctionFieldElement(FieldElement):
         We show that this matrix does indeed work as expected when making a
         vector space from a function field::
 
-            sage: # needs sage.modules sage.rings.function_field
+            sage: # needs sage.rings.function_field
             sage: K.<x> = FunctionField(QQ)
             sage: R.<y> = K[]
             sage: L.<y> = K.extension(y^5 - (x^3 + 2*x*y + 1/x))
@@ -254,7 +254,7 @@ cdef class FunctionFieldElement(FieldElement):
 
             sage: K.<x> = FunctionField(QQ); R.<y> = K[]
             sage: L.<y> = K.extension(y^2 - x*y + 4*x^3)                                # needs sage.rings.function_field
-            sage: y.trace()                                                             # needs sage.modules sage.rings.function_field
+            sage: y.trace()                                                             # needs sage.rings.function_field
             x
         """
         return self.matrix().trace()
@@ -267,7 +267,7 @@ cdef class FunctionFieldElement(FieldElement):
 
             sage: K.<x> = FunctionField(QQ); R.<y> = K[]
             sage: L.<y> = K.extension(y^2 - x*y + 4*x^3)                                # needs sage.rings.function_field
-            sage: y.norm()                                                              # needs sage.modules sage.rings.function_field
+            sage: y.norm()                                                              # needs sage.rings.function_field
             4*x^3
 
         The norm is relative::
@@ -275,9 +275,9 @@ cdef class FunctionFieldElement(FieldElement):
             sage: K.<x> = FunctionField(QQ); R.<y> = K[]
             sage: L.<y> = K.extension(y^2 - x*y + 4*x^3); R.<z> = L[]                   # needs sage.rings.function_field
             sage: M.<z> = L.extension(z^3 - y^2*z + x)                                  # needs sage.rings.function_field
-            sage: z.norm()                                                              # needs sage.modules sage.rings.function_field
+            sage: z.norm()                                                              # needs sage.rings.function_field
             -x
-            sage: z.norm().parent()                                                     # needs sage.modules sage.rings.function_field
+            sage: z.norm().parent()                                                     # needs sage.rings.function_field
             Function field in y defined by y^2 - x*y + 4*x^3
         """
         return self.matrix().determinant()
@@ -326,13 +326,15 @@ cdef class FunctionFieldElement(FieldElement):
         EXAMPLES::
 
             sage: K.<x> = FunctionField(QQ); R.<y> = K[]
-            sage: L.<y> = K.extension(y^2 - x*y + 4*x^3); R.<z> = L[]                   # needs sage.rings.function_field
-            sage: M.<z> = L.extension(z^3 - y^2*z + x)                                  # needs sage.rings.function_field
             sage: x.characteristic_polynomial('W')                                      # needs sage.modules
             W - x
-            sage: y.characteristic_polynomial('W')                                      # needs sage.modules sage.rings.function_field
+
+            sage: # needs sage.rings.function_field
+            sage: L.<y> = K.extension(y^2 - x*y + 4*x^3); R.<z> = L[]
+            sage: M.<z> = L.extension(z^3 - y^2*z + x)
+            sage: y.characteristic_polynomial('W')
             W^2 - x*W + 4*x^3
-            sage: z.characteristic_polynomial('W')                                      # needs sage.modules sage.rings.function_field
+            sage: z.characteristic_polynomial('W')
             W^3 + (-x*y + 4*x^3)*W + x
         """
         return self.matrix().characteristic_polynomial(*args, **kwds)
@@ -347,13 +349,15 @@ cdef class FunctionFieldElement(FieldElement):
         EXAMPLES::
 
             sage: K.<x> = FunctionField(QQ); R.<y> = K[]
-            sage: L.<y> = K.extension(y^2 - x*y + 4*x^3); R.<z> = L[]                   # needs sage.rings.function_field
-            sage: M.<z> = L.extension(z^3 - y^2*z + x)                                  # needs sage.rings.function_field
             sage: x.minimal_polynomial('W')                                             # needs sage.modules
             W - x
-            sage: y.minimal_polynomial('W')                                             # needs sage.modules sage.rings.function_field
+
+            sage: # needs sage.rings.function_field
+            sage: L.<y> = K.extension(y^2 - x*y + 4*x^3); R.<z> = L[]
+            sage: M.<z> = L.extension(z^3 - y^2*z + x)
+            sage: y.minimal_polynomial('W')
             W^2 - x*W + 4*x^3
-            sage: z.minimal_polynomial('W')                                             # needs sage.modules sage.rings.function_field
+            sage: z.minimal_polynomial('W')
             W^3 + (-x*y + 4*x^3)*W + x
         """
         return self.matrix().minimal_polynomial(*args, **kwds)
@@ -366,7 +370,7 @@ cdef class FunctionFieldElement(FieldElement):
 
         EXAMPLES::
 
-            sage: # needs sage.modules sage.rings.function_field
+            sage: # needs sage.rings.function_field
             sage: K.<x> = FunctionField(QQ); R.<y> = K[]
             sage: L.<y> = K.extension(y^2 - x*y + 4*x^3)
             sage: y.is_integral()
@@ -396,7 +400,7 @@ cdef class FunctionFieldElement(FieldElement):
 
             sage: K.<x> = FunctionField(GF(4)); _.<Y> = K[]                             # needs sage.rings.finite_rings
             sage: L.<y> = K.extension(Y^2 + Y + x +1/x)                                 # needs sage.rings.finite_rings sage.rings.function_field
-            sage: (y^3 + x).differential()                                              # needs sage.modules sage.rings.finite_rings sage.rings.function_field
+            sage: (y^3 + x).differential()                                              # needs sage.rings.finite_rings sage.rings.function_field
             (((x^2 + 1)/x^2)*y + (x^4 + x^3 + 1)/x^3) d(x)
 
         TESTS:
@@ -404,16 +408,17 @@ cdef class FunctionFieldElement(FieldElement):
         Verify that :issue:`27712` is resolved::
 
             sage: K.<x> = FunctionField(GF(31))
-            sage: R.<y> = K[]
-            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^2 - y)                                          # needs sage.rings.function_field
-
             sage: x.differential()                                                      # needs sage.modules
             d(x)
-            sage: y.differential()                                                      # needs sage.modules sage.rings.function_field
+
+            sage: # needs sage.rings.function_field
+            sage: R.<y> = K[]
+            sage: L.<y> = K.extension(y^2 - x)
+            sage: R.<z> = L[]
+            sage: M.<z> = L.extension(z^2 - y)
+            sage: y.differential()
             (16/x*y) d(x)
-            sage: z.differential()                                                      # needs sage.modules sage.rings.function_field
+            sage: z.differential()
             (8/x*z) d(x)
         """
         F = self.parent()
@@ -436,7 +441,7 @@ cdef class FunctionFieldElement(FieldElement):
 
             sage: K.<x> = FunctionField(GF(4)); _.<Y> = K[]                             # needs sage.rings.finite_rings
             sage: L.<y> = K.extension(Y^2 + Y + x + 1/x)                                # needs sage.rings.finite_rings sage.rings.function_field
-            sage: (y^3 + x).derivative()                                                # needs sage.modules sage.rings.finite_rings sage.rings.function_field
+            sage: (y^3 + x).derivative()                                                # needs sage.rings.finite_rings sage.rings.function_field
             ((x^2 + 1)/x^2)*y + (x^4 + x^3 + 1)/x^3
         """
         D = self.parent().derivation()
@@ -458,14 +463,14 @@ cdef class FunctionFieldElement(FieldElement):
 
             sage: K.<t> = FunctionField(GF(2))
             sage: f = t^2
-            sage: f.higher_derivative(2)                                                # needs sage.modules sage.rings.function_field
+            sage: f.higher_derivative(2)                                                # needs sage.rings.function_field
             1
 
         ::
 
             sage: K.<x> = FunctionField(GF(4)); _.<Y> = K[]                             # needs sage.rings.finite_rings
             sage: L.<y> = K.extension(Y^2 + Y + x + 1/x)                                # needs sage.rings.finite_rings sage.rings.function_field
-            sage: (y^3 + x).higher_derivative(2)                                        # needs sage.modules sage.rings.finite_rings sage.rings.function_field
+            sage: (y^3 + x).higher_derivative(2)                                        # needs sage.rings.finite_rings sage.rings.function_field
             1/x^3*y + (x^6 + x^4 + x^3 + x^2 + x + 1)/x^5
         """
         D = self.parent().higher_derivation()
@@ -489,7 +494,7 @@ cdef class FunctionFieldElement(FieldElement):
 
             sage: K.<x> = FunctionField(GF(2)); _.<Y> = K[]
             sage: L.<y> = K.extension(Y^2 + Y + x + 1/x)                                # needs sage.rings.function_field
-            sage: y.divisor()                                                           # needs sage.modules sage.rings.function_field
+            sage: y.divisor()                                                           # needs sage.rings.function_field
             - Place (1/x, 1/x*y)
              - Place (x, x*y)
              + 2*Place (x + 1, x*y)
@@ -517,7 +522,7 @@ cdef class FunctionFieldElement(FieldElement):
 
             sage: K.<x> = FunctionField(GF(4)); _.<Y> = K[]                             # needs sage.rings.finite_rings
             sage: L.<y> = K.extension(Y^2 + Y + x + 1/x)                                # needs sage.rings.finite_rings sage.rings.function_field
-            sage: (x/y).divisor_of_zeros()                                              # needs sage.modules sage.rings.finite_rings sage.rings.function_field
+            sage: (x/y).divisor_of_zeros()                                              # needs sage.rings.finite_rings sage.rings.function_field
             3*Place (x, x*y)
         """
         if self.is_zero():
@@ -544,7 +549,7 @@ cdef class FunctionFieldElement(FieldElement):
 
             sage: K.<x> = FunctionField(GF(4)); _.<Y> = K[]                             # needs sage.rings.finite_rings
             sage: L.<y> = K.extension(Y^2 + Y + x + 1/x)                                # needs sage.rings.finite_rings sage.rings.function_field
-            sage: (x/y).divisor_of_poles()                                              # needs sage.modules sage.rings.finite_rings sage.rings.function_field
+            sage: (x/y).divisor_of_poles()                                              # needs sage.rings.finite_rings sage.rings.function_field
             Place (1/x, 1/x*y) + 2*Place (x + 1, x*y)
         """
         if self.is_zero():
@@ -570,7 +575,7 @@ cdef class FunctionFieldElement(FieldElement):
 
             sage: K.<x> = FunctionField(GF(4)); _.<Y> = K[]                             # needs sage.rings.finite_rings
             sage: L.<y> = K.extension(Y^2 + Y + x + 1/x)                                # needs sage.rings.finite_rings sage.rings.function_field
-            sage: (x/y).zeros()                                                         # needs sage.modules sage.rings.finite_rings sage.rings.function_field
+            sage: (x/y).zeros()                                                         # needs sage.rings.finite_rings sage.rings.function_field
             [Place (x, x*y)]
         """
         return self.divisor_of_zeros().support()
@@ -590,7 +595,7 @@ cdef class FunctionFieldElement(FieldElement):
 
             sage: K.<x> = FunctionField(GF(4)); _.<Y> = K[]                             # needs sage.rings.finite_rings
             sage: L.<y> = K.extension(Y^2 + Y + x + 1/x)                                # needs sage.rings.finite_rings sage.rings.function_field
-            sage: (x/y).poles()                                                         # needs sage.modules sage.rings.finite_rings sage.rings.function_field
+            sage: (x/y).poles()                                                         # needs sage.rings.finite_rings sage.rings.function_field
             [Place (1/x, 1/x*y), Place (x + 1, x*y)]
         """
         return self.divisor_of_poles().support()
@@ -607,8 +612,8 @@ cdef class FunctionFieldElement(FieldElement):
 
             sage: K.<x> = FunctionField(GF(2)); _.<Y> = K[]
             sage: L.<y> = K.extension(Y^2 + Y + x + 1/x)                                # needs sage.rings.function_field
-            sage: p = L.places_infinite()[0]                                            # needs sage.modules sage.rings.function_field
-            sage: y.valuation(p)                                                        # needs sage.modules sage.rings.function_field
+            sage: p = L.places_infinite()[0]                                            # needs sage.rings.function_field
+            sage: y.valuation(p)                                                        # needs sage.rings.function_field
             -1
 
         ::
diff --git a/src/sage/rings/function_field/element_polymod.pyx b/src/sage/rings/function_field/element_polymod.pyx
index 7a75bfe978e..55e887ea491 100644
--- a/src/sage/rings/function_field/element_polymod.pyx
+++ b/src/sage/rings/function_field/element_polymod.pyx
@@ -1,4 +1,4 @@
-# sage.doctest: optional - sage.rings.function_field
+# sage.doctest: needs sage.rings.function_field
 r"""
 Elements of function fields: extension
 """
diff --git a/src/sage/rings/function_field/element_rational.pyx b/src/sage/rings/function_field/element_rational.pyx
index 40d0d9734ef..5ad0d81341d 100644
--- a/src/sage/rings/function_field/element_rational.pyx
+++ b/src/sage/rings/function_field/element_rational.pyx
@@ -74,10 +74,11 @@ cdef class FunctionFieldElement_rational(FunctionFieldElement):
             sage: K.<t> = FunctionField(GF(7))
             sage: t.element()
             t
-            sage: type(t.element())                                                     # needs sage.rings.finite_rings
+            sage: type(t.element())                                                     # needs sage.libs.ntl
             <... 'sage.rings.fraction_field_FpT.FpTElement'>
 
-            sage: K.<t> = FunctionField(GF(131101))                                     # needs sage.libs.pari
+            sage: # needs sage.rings.finite_rings
+            sage: K.<t> = FunctionField(GF(131101))
             sage: t.element()
             t
             sage: type(t.element())
@@ -392,9 +393,9 @@ cdef class FunctionFieldElement_rational(FunctionFieldElement):
             True
             sage: f.is_nth_power(3)                                                     # needs sage.modules
             False
-            sage: (f^3).is_nth_power(3)
+            sage: (f^3).is_nth_power(3)                                                 # needs sage.modules
             True
-            sage: (f^9).is_nth_power(-9)
+            sage: (f^9).is_nth_power(-9)                                                # needs sage.modules
             True
         """
         if n == 1:
@@ -437,7 +438,6 @@ cdef class FunctionFieldElement_rational(FunctionFieldElement):
 
         EXAMPLES::
 
-            sage: # needs sage.rings.finite_rings
             sage: K.<x> = FunctionField(GF(3))
             sage: f = (x+1)/(x+2)
             sage: f.nth_root(1)
@@ -446,9 +446,9 @@ cdef class FunctionFieldElement_rational(FunctionFieldElement):
             Traceback (most recent call last):
             ...
             ValueError: element is not an n-th power
-            sage: (f^3).nth_root(3)
+            sage: (f^3).nth_root(3)                                                     # needs sage.modules
             (x + 1)/(x + 2)
-            sage: (f^9).nth_root(-9)
+            sage: (f^9).nth_root(-9)                                                    # needs sage.modules
             (x + 2)/(x + 1)
         """
         if n == 0:
diff --git a/src/sage/rings/function_field/function_field.py b/src/sage/rings/function_field/function_field.py
index 5e8105db36a..315f58cdc39 100644
--- a/src/sage/rings/function_field/function_field.py
+++ b/src/sage/rings/function_field/function_field.py
@@ -190,7 +190,7 @@
 
 The gap numbers for Weierstrass places are of course not ordinary::
 
-    sage: # needs sage.modules sage.rings.function_field
+    sage: # needs sage.rings.function_field
     sage: p1,p2,p3 = L.weierstrass_places()[:3]
     sage: p1.gaps()
     [1, 2, 4]
@@ -532,9 +532,9 @@ def order(self, x, check=True):
             sage: O.basis()                                                             # needs sage.modules
             (1, y, y^2)
 
-            sage: Z = K.order(x); Z                                                     # needs sage.modules sage.rings.function_field
+            sage: Z = K.order(x); Z                                                     # needs sage.rings.function_field
             Order in Rational function field in x over Rational Field
-            sage: Z.basis()                                                             # needs sage.modules sage.rings.function_field
+            sage: Z.basis()                                                             # needs sage.rings.function_field
             (1,)
 
         Orders with multiple generators are not yet supported::
@@ -619,7 +619,7 @@ def order_infinite(self, x, check=True):
 
             sage: K.<x> = FunctionField(QQ); R.<y> = K[]
             sage: L.<y> = K.extension(y^3 + x^3 + 4*x + 1)                              # needs sage.rings.function_field
-            sage: L.order_infinite(y)           # not implemented                       # needs sage.modules sage.rings.function_field
+            sage: L.order_infinite(y)           # not implemented                       # needs sage.rings.function_field
 
             sage: Z = K.order(x); Z                                                     # needs sage.modules
             Order in Rational function field in x over Rational Field
@@ -1016,7 +1016,7 @@ def space_of_differentials(self):
 
             sage: K.<x> = FunctionField(GF(5)); _.<Y> = K[]
             sage: L.<y> = K.extension(Y^3 - (x^3 - 1)/(x^3 - 2))                        # needs sage.rings.function_field
-            sage: L.space_of_differentials()                                            # needs sage.modules sage.rings.function_field
+            sage: L.space_of_differentials()                                            # needs sage.rings.function_field
             Space of differentials of Function field in y
              defined by y^3 + (4*x^3 + 1)/(x^3 + 3)
         """
@@ -1040,7 +1040,7 @@ def space_of_holomorphic_differentials(self):
 
             sage: K.<x> = FunctionField(GF(5)); _.<Y> = K[]
             sage: L.<y> = K.extension(Y^3 - (x^3 - 1)/(x^3 - 2))                        # needs sage.rings.function_field
-            sage: L.space_of_holomorphic_differentials()                                # needs sage.modules sage.rings.function_field
+            sage: L.space_of_holomorphic_differentials()                                # needs sage.rings.function_field
             (Vector space of dimension 4 over Finite Field of size 5,
              Linear map:
                From: Vector space of dimension 4 over Finite Field of size 5
@@ -1067,7 +1067,7 @@ def basis_of_holomorphic_differentials(self):
 
             sage: K.<x> = FunctionField(GF(5)); _.<Y> = K[]
             sage: L.<y> = K.extension(Y^3 - (x^3 - 1)/(x^3 - 2))                        # needs sage.rings.function_field
-            sage: L.basis_of_holomorphic_differentials()                                # needs sage.modules sage.rings.function_field
+            sage: L.basis_of_holomorphic_differentials()                                # needs sage.rings.function_field
             [((x/(x^3 + 4))*y) d(x),
              ((1/(x^3 + 4))*y) d(x),
              ((x/(x^3 + 4))*y^2) d(x),
@@ -1089,12 +1089,12 @@ def divisor_group(self):
 
             sage: _.<Y> = K[]
             sage: L.<y> = K.extension(Y^3 - (t^3 - 1)/(t^3 - 2))                        # needs sage.rings.function_field
-            sage: L.divisor_group()                                                     # needs sage.modules sage.rings.function_field
+            sage: L.divisor_group()                                                     # needs sage.rings.function_field
             Divisor group of Function field in y defined by y^3 + (-t^3 + 1)/(t^3 - 2)
 
             sage: K.<x> = FunctionField(GF(5)); _.<Y> = K[]
             sage: L.<y> = K.extension(Y^3 - (x^3 - 1)/(x^3 - 2))                        # needs sage.rings.function_field
-            sage: L.divisor_group()                                                     # needs sage.modules sage.rings.function_field
+            sage: L.divisor_group()                                                     # needs sage.rings.function_field
             Divisor group of Function field in y defined by y^3 + (4*x^3 + 1)/(x^3 + 3)
         """
         from .divisor import DivisorGroup
diff --git a/src/sage/rings/function_field/function_field_polymod.py b/src/sage/rings/function_field/function_field_polymod.py
index ef72935eba6..fd8c975e682 100644
--- a/src/sage/rings/function_field/function_field_polymod.py
+++ b/src/sage/rings/function_field/function_field_polymod.py
@@ -1,4 +1,4 @@
-# sage.doctest: optional - sage.rings.function_field
+# sage.doctest: needs sage.rings.function_field
 r"""
 Function Fields: extension
 """
diff --git a/src/sage/rings/function_field/function_field_rational.py b/src/sage/rings/function_field/function_field_rational.py
index 2226c086b00..bb2075b1ecf 100644
--- a/src/sage/rings/function_field/function_field_rational.py
+++ b/src/sage/rings/function_field/function_field_rational.py
@@ -102,7 +102,7 @@ class RationalFunctionField(FunctionField):
         sage: R.<x> = FunctionField(QQ)
         sage: L.<y> = R[]
         sage: F.<y> = R.extension(y^2 - (x^2+1))                                        # needs sage.rings.function_field
-        sage: (y/x).divisor()                                                           # needs sage.modules sage.rings.function_field
+        sage: (y/x).divisor()                                                           # needs sage.rings.function_field
         - Place (x, y - 1)
          - Place (x, y + 1)
          + Place (x^2 + 1, y)
@@ -112,15 +112,13 @@ class RationalFunctionField(FunctionField):
         sage: NF.<i> = NumberField(z^2 + 1)
         sage: R.<x> = FunctionField(NF)
         sage: L.<y> = R[]
-        sage: F.<y> = R.extension(y^2 - (x^2+1))                                        # needs sage.modules sage.rings.function_field
-
-        sage: (x/y*x.differential()).divisor()                                          # needs sage.modules sage.rings.function_field sage.rings.number_field
+        sage: F.<y> = R.extension(y^2 - (x^2+1))                                        # needs sage.rings.function_field
+        sage: (x/y*x.differential()).divisor()                                          # needs sage.rings.function_field
         -2*Place (1/x, 1/x*y - 1)
          - 2*Place (1/x, 1/x*y + 1)
          + Place (x, y - 1)
          + Place (x, y + 1)
-
-        sage: (x/y).divisor()                                                           # needs sage.modules sage.rings.function_field sage.rings.number_field
+        sage: (x/y).divisor()                                                           # needs sage.rings.function_field
         - Place (x - i, y)
          + Place (x, y - 1)
          + Place (x, y + 1)
@@ -135,7 +133,6 @@ def __init__(self, constant_field, names, category=None):
 
         EXAMPLES::
 
-
             sage: K.<t> = FunctionField(CC); K                                          # needs sage.rings.real_mpfr
             Rational function field in t over Complex Field with 53 bits of precision
             sage: TestSuite(K).run()            # long time (5s)                        # needs sage.rings.real_mpfr
diff --git a/src/sage/rings/function_field/ideal.py b/src/sage/rings/function_field/ideal.py
index 47fba9754f7..00450c60533 100644
--- a/src/sage/rings/function_field/ideal.py
+++ b/src/sage/rings/function_field/ideal.py
@@ -455,14 +455,14 @@ def divisor(self):
 
         EXAMPLES::
 
-            sage: # needs sage.rings.finite_rings
+            sage: # needs sage.modules sage.rings.finite_rings
             sage: K.<x> = FunctionField(GF(4))
             sage: O = K.maximal_order()
             sage: I = O.ideal(x*(x + 1)^2/(x^2 + x + 1))
             sage: I.divisor()
             Place (x) + 2*Place (x + 1) - Place (x + z2) - Place (x + z2 + 1)
 
-            sage: # needs sage.rings.finite_rings
+            sage: # needs sage.modules sage.rings.finite_rings
             sage: Oinf = K.maximal_order_infinite()
             sage: I = Oinf.ideal((x + 1)/(x^3 + 1))
             sage: I.divisor()
@@ -528,7 +528,7 @@ def divisor_of_zeros(self):
             sage: I.divisor_of_zeros()
             2*Place (1/x)
 
-            sage: # needs sage.modules sage.rings.function_field
+            sage: # needs sage.rings.function_field
             sage: K.<x> = FunctionField(GF(2)); _.<Y> = K[]
             sage: L.<y> = K.extension(Y^2 + Y + x + 1/x)
             sage: O = L.maximal_order()
@@ -565,7 +565,7 @@ def divisor_of_poles(self):
             sage: I.divisor_of_poles()
             0
 
-            sage: # needs sage.modules sage.rings.function_field
+            sage: # needs sage.rings.function_field
             sage: K.<x> = FunctionField(GF(2)); _.<Y> = K[]
             sage: L.<y> = K.extension(Y^2 + Y + x + 1/x)
             sage: O = L.maximal_order()
diff --git a/src/sage/rings/function_field/ideal_polymod.py b/src/sage/rings/function_field/ideal_polymod.py
index da45bc508cf..83a1370e493 100644
--- a/src/sage/rings/function_field/ideal_polymod.py
+++ b/src/sage/rings/function_field/ideal_polymod.py
@@ -1,4 +1,4 @@
-# sage.doctest: optional - sage.rings.function_field
+# sage.doctest: needs sage.rings.function_field
 r"""
 Ideals of function fields: extension
 """
diff --git a/src/sage/rings/function_field/maps.py b/src/sage/rings/function_field/maps.py
index dedd3d2a998..2863a953f20 100644
--- a/src/sage/rings/function_field/maps.py
+++ b/src/sage/rings/function_field/maps.py
@@ -72,7 +72,7 @@ class FunctionFieldVectorSpaceIsomorphism(Morphism):
 
     EXAMPLES::
 
-        sage: # needs sage.modules sage.rings.function_field
+        sage: # needs sage.rings.function_field
         sage: K.<x> = FunctionField(QQ); R.<y> = K[]
         sage: L.<y> = K.extension(y^2 - x*y + 4*x^3)
         sage: V, f, t = L.vector_space()
@@ -85,7 +85,7 @@ def _repr_(self) -> str:
 
         EXAMPLES::
 
-            sage: # needs sage.modules sage.rings.function_field
+            sage: # needs sage.rings.function_field
             sage: K.<x> = FunctionField(QQ); R.<y> = K[]
             sage: L.<y> = K.extension(y^2 - x*y + 4*x^3)
             sage: V, f, t = L.vector_space()
@@ -109,7 +109,7 @@ def is_injective(self) -> bool:
 
         EXAMPLES::
 
-            sage: # needs sage.modules sage.rings.function_field
+            sage: # needs sage.rings.function_field
             sage: K.<x> = FunctionField(QQ); R.<y> = K[]
             sage: L.<y> = K.extension(y^2 - x*y + 4*x^3)
             sage: V, f, t = L.vector_space()
@@ -124,7 +124,7 @@ def is_surjective(self) -> bool:
 
         EXAMPLES::
 
-            sage: # needs sage.modules sage.rings.function_field
+            sage: # needs sage.rings.function_field
             sage: K.<x> = FunctionField(QQ); R.<y> = K[]
             sage: L.<y> = K.extension(y^2 - x*y + 4*x^3)
             sage: V, f, t = L.vector_space()
@@ -191,7 +191,7 @@ class MapVectorSpaceToFunctionField(FunctionFieldVectorSpaceIsomorphism):
 
     EXAMPLES::
 
-        sage: # needs sage.modules sage.rings.function_field
+        sage: # needs sage.rings.function_field
         sage: K.<x> = FunctionField(QQ); R.<y> = K[]
         sage: L.<y> = K.extension(y^2 - x*y + 4*x^3)
         sage: V, f, t = L.vector_space(); f
@@ -203,7 +203,7 @@ def __init__(self, V, K):
         """
         EXAMPLES::
 
-            sage: # needs sage.modules sage.rings.function_field
+            sage: # needs sage.rings.function_field
             sage: K.<x> = FunctionField(QQ); R.<y> = K[]
             sage: L.<y> = K.extension(y^2 - x*y + 4*x^3)
             sage: V, f, t = L.vector_space(); type(f)
@@ -224,7 +224,7 @@ def _call_(self, v):
 
         EXAMPLES::
 
-            sage: # needs sage.modules sage.rings.function_field
+            sage: # needs sage.rings.function_field
             sage: K.<x> = FunctionField(QQ)
             sage: R.<y> = K[]
             sage: L.<y> = K.extension(y^2 - x*y + 4*x^3)
@@ -236,7 +236,7 @@ def _call_(self, v):
 
         Test that this map is a bijection for some random inputs::
 
-            sage: # needs sage.modules sage.rings.function_field
+            sage: # needs sage.rings.function_field
             sage: R.<z> = L[]
             sage: M.<z> = L.extension(z^3 - y - x)
             sage: for F in [K, L, M]:
@@ -270,7 +270,7 @@ def domain(self):
 
         EXAMPLES::
 
-            sage: # needs sage.modules sage.rings.function_field
+            sage: # needs sage.rings.function_field
             sage: K.<x> = FunctionField(QQ); R.<y> = K[]
             sage: L.<y> = K.extension(y^2 - x*y + 4*x^3)
             sage: V, f, t = L.vector_space()
@@ -285,7 +285,7 @@ def codomain(self):
 
         EXAMPLES::
 
-            sage: # needs sage.modules sage.rings.function_field
+            sage: # needs sage.rings.function_field
             sage: K.<x> = FunctionField(QQ); R.<y> = K[]
             sage: L.<y> = K.extension(y^2 - x*y + 4*x^3)
             sage: V, f, t = L.vector_space()
@@ -301,7 +301,7 @@ class MapFunctionFieldToVectorSpace(FunctionFieldVectorSpaceIsomorphism):
 
     EXAMPLES::
 
-        sage: # needs sage.modules sage.rings.function_field
+        sage: # needs sage.rings.function_field
         sage: K.<x> = FunctionField(QQ); R.<y> = K[]
         sage: L.<y> = K.extension(y^2 - x*y + 4*x^3)
         sage: V, f, t = L.vector_space(); t
@@ -321,7 +321,7 @@ def __init__(self, K, V):
 
         EXAMPLES::
 
-            sage: # needs sage.modules sage.rings.function_field
+            sage: # needs sage.rings.function_field
             sage: K.<x> = FunctionField(QQ); R.<y> = K[]
             sage: L.<y> = K.extension(y^2 - x*y + 4*x^3)
             sage: V, f, t = L.vector_space()
@@ -339,7 +339,7 @@ def _call_(self, x):
 
         EXAMPLES::
 
-            sage: # needs sage.modules sage.rings.function_field
+            sage: # needs sage.rings.function_field
             sage: K.<x> = FunctionField(QQ); R.<y> = K[]
             sage: L.<y> = K.extension(y^2 - x*y + 4*x^3)
             sage: V, f, t = L.vector_space()
@@ -350,7 +350,7 @@ def _call_(self, x):
 
         Test that this map is a bijection for some random inputs::
 
-            sage: # needs sage.modules sage.rings.function_field
+            sage: # needs sage.rings.function_field
             sage: R.<z> = L[]
             sage: M.<z> = L.extension(z^3 - y - x)
             sage: for F in [K, L, M]:
diff --git a/src/sage/rings/function_field/order.py b/src/sage/rings/function_field/order.py
index 6ffe40c5faf..0afeaa5f526 100644
--- a/src/sage/rings/function_field/order.py
+++ b/src/sage/rings/function_field/order.py
@@ -274,7 +274,7 @@ def _repr_(self):
 
             sage: K.<x> = FunctionField(GF(2)); R.<t> = PolynomialRing(K)
             sage: F.<y> = K.extension(t^3 - x^2*(x^2+x+1)^2)                            # needs sage.rings.function_field
-            sage: F.maximal_order_infinite()                                            # needs sage.modules sage.rings.function_field
+            sage: F.maximal_order_infinite()                                            # needs sage.rings.function_field
             Maximal infinite order of Function field in y defined by y^3 + x^6 + x^4 + x^2
         """
         return "Maximal infinite order of %s" % (self.function_field(),)
diff --git a/src/sage/rings/function_field/order_polymod.py b/src/sage/rings/function_field/order_polymod.py
index d6831fa7248..ad760aad0b6 100644
--- a/src/sage/rings/function_field/order_polymod.py
+++ b/src/sage/rings/function_field/order_polymod.py
@@ -1,4 +1,4 @@
-# sage.doctest: optional - sage.rings.function_field
+# sage.doctest: needs sage.rings.function_field
 r"""
 Orders of function fields: extension
 """
diff --git a/src/sage/rings/function_field/order_rational.py b/src/sage/rings/function_field/order_rational.py
index 99da2af1ebd..b21712bcf2c 100644
--- a/src/sage/rings/function_field/order_rational.py
+++ b/src/sage/rings/function_field/order_rational.py
@@ -129,7 +129,7 @@ def _residue_field(self, ideal, name=None):
 
         EXAMPLES::
 
-            sage: # needs sage.rings.finite_rings
+            sage: # needs sage.modules sage.rings.finite_rings
             sage: F.<x> = FunctionField(GF(2))
             sage: O = F.maximal_order()
             sage: I = O.ideal(x^2 + x + 1)
@@ -150,7 +150,7 @@ def _residue_field(self, ideal, name=None):
             sage: to_R(e2).parent() is R
             True
 
-            sage: # needs sage.rings.finite_rings
+            sage: # needs sage.modules sage.rings.finite_rings
             sage: F.<x> = FunctionField(GF(2))
             sage: O = F.maximal_order()
             sage: I = O.ideal(x + 1)
@@ -171,20 +171,21 @@ def _residue_field(self, ideal, name=None):
             sage: to_R(e2).parent() is R
             True
 
+            sage: # needs sage.modules sage.rings.number_field
             sage: F.<x> = FunctionField(QQ)
             sage: O = F.maximal_order()
             sage: I = O.ideal(x^2 + x + 1)
-            sage: R, fr_R, to_R = O._residue_field(I)                                               # needs sage.rings.number_field
-            sage: R                                                                                 # needs sage.rings.number_field
+            sage: R, fr_R, to_R = O._residue_field(I)
+            sage: R
             Number Field in a with defining polynomial x^2 + x + 1
-            sage: e1, e2 = fr_R(R.random_element()), fr_R(R.random_element())                       # needs sage.rings.number_field
-            sage: to_R(e1 * e2) == to_R(e1) * to_R(e2)                                              # needs sage.rings.number_field
+            sage: e1, e2 = fr_R(R.random_element()), fr_R(R.random_element())
+            sage: to_R(e1 * e2) == to_R(e1) * to_R(e2)
             True
-            sage: to_R(e1 + e2) == to_R(e1) + to_R(e2)                                              # needs sage.rings.number_field
+            sage: to_R(e1 + e2) == to_R(e1) + to_R(e2)
             True
-            sage: to_R(e1).parent() is R                                                            # needs sage.rings.number_field
+            sage: to_R(e1).parent() is R
             True
-            sage: to_R(e2).parent() is R                                                            # needs sage.rings.number_field
+            sage: to_R(e2).parent() is R
             True
 
             sage: F.<x> = FunctionField(QQ)
diff --git a/src/sage/rings/function_field/place.py b/src/sage/rings/function_field/place.py
index efff8d4305e..a17c97b7316 100644
--- a/src/sage/rings/function_field/place.py
+++ b/src/sage/rings/function_field/place.py
@@ -252,7 +252,7 @@ def __radd__(self, other):
 
             sage: k.<a> = GF(2)
             sage: K.<x> = FunctionField(k)
-            sage: sum(K.places_finite())                                                # needs sage.libs.pari
+            sage: sum(K.places_finite())                                                # needs sage.libs.pari sage.modules
             Place (x) + Place (x + 1)
 
         Note that this does not work, as wanted::
diff --git a/src/sage/rings/function_field/place_polymod.py b/src/sage/rings/function_field/place_polymod.py
index f345c31129e..ee9e8de5874 100644
--- a/src/sage/rings/function_field/place_polymod.py
+++ b/src/sage/rings/function_field/place_polymod.py
@@ -1,4 +1,4 @@
-# sage.doctest: optional - sage.rings.function_field
+# sage.doctest: needs sage.rings.function_field
 """
 Places of function fields: extension
 """
diff --git a/src/sage/rings/function_field/place_rational.py b/src/sage/rings/function_field/place_rational.py
index 9b98397ba90..31ffd6a40b0 100644
--- a/src/sage/rings/function_field/place_rational.py
+++ b/src/sage/rings/function_field/place_rational.py
@@ -1,4 +1,4 @@
-# sage.doctest: optional - sage.rings.finite_rings       (because all doctests use finite fields)
+# sage.doctest: needs sage.rings.finite_rings       (because all doctests use finite fields)
 """
 Places of function fields: rational
 """
@@ -102,6 +102,7 @@ def _residue_field(self, name=None):
 
         EXAMPLES::
 
+            sage: # needs sage.modules
             sage: F.<x> = FunctionField(GF(2))
             sage: O = F.maximal_order()
             sage: i = O.ideal(x^2 + x + 1)
diff --git a/src/sage/rings/function_field/valuation_ring.py b/src/sage/rings/function_field/valuation_ring.py
index 81fc97d3324..e1fe9751b0b 100644
--- a/src/sage/rings/function_field/valuation_ring.py
+++ b/src/sage/rings/function_field/valuation_ring.py
@@ -1,5 +1,5 @@
-# sage.doctest: optional - sage.rings.finite_rings
-# sage.doctest: optional - sage.rings.function_field
+# sage.doctest: needs sage.rings.finite_rings
+# sage.doctest: needs sage.rings.function_field
 r"""
 Valuation rings of function fields
 
diff --git a/src/sage/rings/polynomial/binary_form_reduce.py b/src/sage/rings/polynomial/binary_form_reduce.py
index ff36ec13ab0..6afb11155cf 100644
--- a/src/sage/rings/polynomial/binary_form_reduce.py
+++ b/src/sage/rings/polynomial/binary_form_reduce.py
@@ -25,10 +25,8 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.calculus.functions import jacobian
-from sage.functions.hyperbolic import cosh, sinh
-from sage.functions.log import exp
 from sage.matrix.constructor import matrix
+from sage.misc.lazy_import import lazy_import
 from sage.misc.misc_c import prod
 from sage.modules.free_module_element import vector
 from sage.rings.cc import CC
@@ -40,6 +38,10 @@
 from sage.rings.rational_field import QQ
 from sage.rings.real_mpfr import RealField
 
+lazy_import("sage.calculus.functions", "jacobian")
+lazy_import("sage.functions.hyperbolic", ["cosh", "sinh"])
+lazy_import("sage.functions.log", "exp")
+
 
 def covariant_z0(F, z0_cov=False, prec=53, emb=None, error_limit=0.000001):
     r"""
diff --git a/src/sage/rings/polynomial/ideal.py b/src/sage/rings/polynomial/ideal.py
index 011cb860290..9eba00860b5 100644
--- a/src/sage/rings/polynomial/ideal.py
+++ b/src/sage/rings/polynomial/ideal.py
@@ -92,8 +92,9 @@ def change_ring(self, R):
         EXAMPLES::
 
             sage: R.<q> = QQ[]
-            sage: I = R.ideal([q^2+q-1])
-            sage: I.change_ring(RR['q'])
-            Principal ideal (q^2 + q - 1.00000000000000) of Univariate Polynomial Ring in q over Real Field with 53 bits of precision
+            sage: I = R.ideal([q^2 + q - 1])
+            sage: I.change_ring(RR['q'])                                                # needs sage.rings.real_mpfr
+            Principal ideal (q^2 + q - 1.00000000000000) of
+             Univariate Polynomial Ring in q over Real Field with 53 bits of precision
         """
         return R.ideal(self.gens())
diff --git a/src/sage/rings/polynomial/polynomial_element.pyx b/src/sage/rings/polynomial/polynomial_element.pyx
index 1270c42ce2a..1bddae9ebfc 100644
--- a/src/sage/rings/polynomial/polynomial_element.pyx
+++ b/src/sage/rings/polynomial/polynomial_element.pyx
@@ -6538,8 +6538,8 @@ cdef class Polynomial(CommutativePolynomial):
 
         TESTS::
 
-            sage: a = RIF['x'](1/3)
-            sage: (a - a).exponents()
+            sage: a = RIF['x'](1/3)                                                     # needs sage.rings.real_interval_field
+            sage: (a - a).exponents()                                                   # needs sage.rings.real_interval_field
             [0]
         """
         cdef Py_ssize_t i
@@ -7944,11 +7944,12 @@ cdef class Polynomial(CommutativePolynomial):
 
         The following examples show that :issue:`11782` has been fixed::
 
-            sage: var('x')                                                              # needs sage.symbolic
+            sage: # needs sage.libs.pari sage.symbolic
+            sage: var('x')
             x
-            sage: ZZ.quo(81)['x'](3*x^2 + 3*x + 3).discriminant()                       # needs sage.libs.pari sage.symbolic
+            sage: ZZ.quo(81)['x'](3*x^2 + 3*x + 3).discriminant()
             54
-            sage: ZZ.quo(9)['x'](2*x^3 + x^2 + x).discriminant()                        # needs sage.libs.pari sage.symbolic
+            sage: ZZ.quo(9)['x'](2*x^3 + x^2 + x).discriminant()
             2
 
         This was fixed by :issue:`15422`::
@@ -8487,7 +8488,7 @@ cdef class Polynomial(CommutativePolynomial):
 
         ::
 
-            sage: # needs sage.rings.complex_double sage.rings.real_mpfr
+            sage: # needs numpy sage.rings.complex_double sage.rings.real_mpfr
             sage: rflds = (RR, RDF, RealField(100))
             sage: cflds = (CC, CDF, ComplexField(100))
             sage: def cross(a, b):
@@ -9773,6 +9774,8 @@ cdef class Polynomial(CommutativePolynomial):
             sage: d = z^4 + (2*t + 4)*z^3 + (-t + 5)*z^2 + (t^2 + 2)*z + t^2 + 2*t + 1
             sage: prec = 9
             sage: x = n.subs(z=w)/d.subs(z=w) + O(w^prec)
+
+            sage: # needs sage.libs.flint (otherwise timeout)
             sage: nc, dc = Pz(x.list()).rational_reconstruction(z^prec)
             sage: (nc, dc) == (n, d)
             True
diff --git a/src/sage/rings/polynomial/polynomial_ring.py b/src/sage/rings/polynomial/polynomial_ring.py
index bdcfb2de0ae..d0d2d1241ab 100644
--- a/src/sage/rings/polynomial/polynomial_ring.py
+++ b/src/sage/rings/polynomial/polynomial_ring.py
@@ -3623,8 +3623,12 @@ def irreducible_element(self, n, algorithm=None):
             return self(conway_polynomial(p, n))
         elif algorithm == "first_lexicographic":
             if p == 2:
-                from .polynomial_gf2x import GF2X_BuildIrred_list
-                return self(GF2X_BuildIrred_list(n))
+                try:
+                    from .polynomial_gf2x import GF2X_BuildIrred_list
+                except ImportError:
+                    pass
+                else:
+                    return self(GF2X_BuildIrred_list(n))
             else:
                 # Fallback to PolynomialRing_dense_finite_field.irreducible_element
                 pass
@@ -3638,8 +3642,12 @@ def irreducible_element(self, n, algorithm=None):
                 raise NotImplementedError("'minimal_weight' option only implemented for p = 2")
         elif algorithm == "random":
             if p == 2:
-                from .polynomial_gf2x import GF2X_BuildRandomIrred_list
-                return self(GF2X_BuildRandomIrred_list(n))
+                try:
+                    from .polynomial_gf2x import GF2X_BuildRandomIrred_list
+                except ImportError:
+                    pass
+                else:
+                    return self(GF2X_BuildRandomIrred_list(n))
             else:
                 pass
 
diff --git a/src/sage/rings/qqbar.py b/src/sage/rings/qqbar.py
index f6d391679a6..d356edf742f 100644
--- a/src/sage/rings/qqbar.py
+++ b/src/sage/rings/qqbar.py
@@ -3776,9 +3776,13 @@ def _repr_(self):
         if isinstance(self._descr, ANExtensionElement) and self._descr._generator is QQbar_I_generator:
             return repr(self._descr._value)
         if self.parent().options.display_format == 'radical':
-            radical = self.radical_expression()
-            if radical is not self:
-                return repr(radical)
+            try:
+                radical = self.radical_expression()
+            except ImportError:
+                pass
+            else:
+                if radical is not self:
+                    return repr(radical)
         if self.parent() is QQbar:
             return repr(CIF(self._value))
         else:
@@ -3819,9 +3823,13 @@ def _latex_(self):
         if isinstance(self._descr, ANExtensionElement) and self._descr._generator is QQbar_I_generator:
             return latex(self._descr._value)
         if self.parent().options.display_format == 'radical':
-            radical = self.radical_expression()
-            if radical is not self:
-                return latex(radical)
+            try:
+                radical = self.radical_expression()
+            except ImportError:
+                pass
+            else:
+                if radical is not self:
+                    return latex(radical)
         return repr(self).replace('*I', r' \sqrt{-1}')
 
     def _sage_input_(self, sib, coerce):
diff --git a/src/sage/rings/real_arb.pyx b/src/sage/rings/real_arb.pyx
index 73232348a01..4b34af0e8bf 100644
--- a/src/sage/rings/real_arb.pyx
+++ b/src/sage/rings/real_arb.pyx
@@ -675,12 +675,16 @@ class RealBallField(UniqueRepresentation, sage.rings.abc.RealBallField):
             [-4.733045976388941e+363922934236666733021124 +/- ...e+363922934236666733021108],
             [+/- inf], [+/- inf], [+/- inf], nan]
         """
-        import sage.symbolic.constants
         inf = self(sage.rings.infinity.Infinity)
-        return [self(0), self(1), self(1)/3,
-                -self(2)**(Integer(2)**80),
-                inf, -inf, self.zero().add_error(inf),
-                self.element_class(self, sage.symbolic.constants.NotANumber())]
+        elements = [self(0), self(1), self(1)/3, -self(2)**(Integer(2)**80),
+                    inf, -inf, self.zero().add_error(inf)]
+        try:
+            from sage.symbolic.constants import NotANumber
+        except ImportError:
+            pass
+        else:
+            elements.append(self.element_class(self, NotANumber()))
+        return elements
 
     def _sum_of_products(self, terms):
         r"""
@@ -1421,8 +1425,7 @@ cdef class RealBall(RingElement):
                 raise ValueError("unsupported string format")
         else:
             # the initializers that trigger imports
-            import sage.symbolic.constants
-            import sage.symbolic.expression
+            import sage.rings.infinity
             if isinstance(mid, sage.rings.infinity.AnInfinity):
                 if isinstance(mid, sage.rings.infinity.PlusInfinity):
                     arb_pos_inf(self.value)
@@ -1430,33 +1433,39 @@ cdef class RealBall(RingElement):
                     arb_neg_inf(self.value)
                 else:
                     arb_zero_pm_inf(self.value)
-            elif isinstance(mid, sage.symbolic.constants.Constant):
-                if _do_sig(prec(self)): sig_on()
+            else:
                 try:
-                    if isinstance(mid, sage.symbolic.constants.NotANumber):
-                        arb_indeterminate(self.value)
-                    elif isinstance(mid, sage.symbolic.constants.Pi):
-                        arb_const_pi(self.value, prec(self))
-                    elif isinstance(mid, sage.symbolic.constants.Log2):
-                        arb_const_log2(self.value, prec(self))
-                    elif isinstance(mid, sage.symbolic.constants.Catalan):
-                        arb_const_catalan(self.value, prec(self))
-                    elif isinstance(mid, sage.symbolic.constants.Khinchin):
-                        arb_const_khinchin(self.value, prec(self))
-                    elif isinstance(mid, sage.symbolic.constants.Glaisher):
-                        arb_const_glaisher(self.value, prec(self))
-                    elif isinstance(mid, sage.symbolic.constants.EulerGamma):
-                        arb_const_euler(self.value, prec(self))
-                    else:
-                        raise TypeError("unsupported constant")
-                finally:
+                    import sage.symbolic.constants
+                    import sage.symbolic.expression
+                except ImportError:
+                    raise TypeError("unsupported midpoint type")
+                if isinstance(mid, sage.symbolic.constants.Constant):
+                    if _do_sig(prec(self)): sig_on()
+                    try:
+                        if isinstance(mid, sage.symbolic.constants.NotANumber):
+                            arb_indeterminate(self.value)
+                        elif isinstance(mid, sage.symbolic.constants.Pi):
+                            arb_const_pi(self.value, prec(self))
+                        elif isinstance(mid, sage.symbolic.constants.Log2):
+                            arb_const_log2(self.value, prec(self))
+                        elif isinstance(mid, sage.symbolic.constants.Catalan):
+                            arb_const_catalan(self.value, prec(self))
+                        elif isinstance(mid, sage.symbolic.constants.Khinchin):
+                            arb_const_khinchin(self.value, prec(self))
+                        elif isinstance(mid, sage.symbolic.constants.Glaisher):
+                            arb_const_glaisher(self.value, prec(self))
+                        elif isinstance(mid, sage.symbolic.constants.EulerGamma):
+                            arb_const_euler(self.value, prec(self))
+                        else:
+                            raise TypeError("unsupported constant")
+                    finally:
+                        if _do_sig(prec(self)): sig_off()
+                elif isinstance(mid, sage.symbolic.expression.E):
+                    if _do_sig(prec(self)): sig_on()
+                    arb_const_e(self.value, prec(self))
                     if _do_sig(prec(self)): sig_off()
-            elif isinstance(mid, sage.symbolic.expression.E):
-                if _do_sig(prec(self)): sig_on()
-                arb_const_e(self.value, prec(self))
-                if _do_sig(prec(self)): sig_off()
-            else:
-                raise TypeError("unsupported midpoint type")
+                else:
+                    raise TypeError("unsupported midpoint type")
 
         if rad is not None:
             mag_init(tmpm)