sage.rings.function_field: Update # needs

Author: Matthias Koeppe

src/sage/rings/function_field/function_field_rational.py

@@ -378,9 +378,9 @@ def _factor_univariate_polynomial(self, f, proof=None):
             sage: R.<t> = FunctionField(GF(7))
             sage: S.<X> = R[]
             sage: f = (1/t)*(X^4 - 1/t^2)*(X^3 - t^3)
-            sage: f.factor()
+            sage: f.factor()                                                            # needs sage.libs.pari
             (1/t) * (X + 3*t) * (X + 5*t) * (X + 6*t) * (X^2 + 1/t) * (X^2 + 6/t)
-            sage: f.factor().prod() == f
+            sage: f.factor().prod() == f                                                # needs sage.libs.pari
             True
 
         Factoring over a function field over a non-prime finite field::

src/sage/rings/function_field/ideal.py

@@ -515,20 +515,21 @@ def divisor_of_zeros(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_of_zeros()
             Place (x) + 2*Place (x + 1)
 
+            sage: # needs sage.modules
             sage: K.<x> = FunctionField(GF(2))
             sage: Oinf = K.maximal_order_infinite()
             sage: I = Oinf.ideal((x + 1)/(x^3 + 1))
             sage: I.divisor_of_zeros()
             2*Place (1/x)
 
-            sage: # needs sage.rings.function_field
+            sage: # needs sage.modules 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()
@@ -551,20 +552,21 @@ def divisor_of_poles(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_of_poles()
             Place (x + z2) + Place (x + z2 + 1)
 
+            sage: # needs sage.modules
             sage: K.<x> = FunctionField(GF(2))
             sage: Oinf = K.maximal_order_infinite()
             sage: I = Oinf.ideal((x + 1)/(x^3 + 1))
             sage: I.divisor_of_poles()
             0
 
-            sage: # needs sage.rings.function_field
+            sage: # needs sage.modules 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()
@@ -1022,17 +1024,20 @@ def module(self):
             sage: O = K.maximal_order(); O
             Maximal order of Rational function field in x over Finite Field of size 7
             sage: K.polynomial_ring()
-            Univariate Polynomial Ring in x over Rational function field in x over Finite Field of size 7
+            Univariate Polynomial Ring in x over
+             Rational function field in x over Finite Field of size 7
             sage: I = O.ideal([x^2 + 1, x*(x^2+1)])
             sage: I.gens()
             (x^2 + 1,)
-            sage: I.module()
-            Free module of degree 1 and rank 1 over Maximal order of Rational function field in x over Finite Field of size 7
+            sage: I.module()                                                            # needs sage.modules
+            Free module of degree 1 and rank 1 over
+             Maximal order of Rational function field in x over Finite Field of size 7
             Echelon basis matrix:
             [x^2 + 1]
-            sage: V, from_V, to_V = K.vector_space(); V
-            Vector space of dimension 1 over Rational function field in x over Finite Field of size 7
-            sage: I.module().is_submodule(V)
+            sage: V, from_V, to_V = K.vector_space(); V                                 # needs sage.modules
+            Vector space of dimension 1 over
+             Rational function field in x over Finite Field of size 7
+            sage: I.module().is_submodule(V)                                            # needs sage.modules
             True
         """
         return self._module