./sage -fixdoctests --distribution 'sagemath-modules[pari]' --only-tags --probe all src/sage/rings/function_field/

Author: Matthias Koeppe

src/sage/rings/function_field/differential.py

@@ -151,7 +151,7 @@ def _latex_(self):
 
             sage: # needs sage.rings.finite_rings
             sage: K.<x> = FunctionField(GF(4)); _.<Y> = K[]
-            sage: L.<y> = K.extension(Y^3 + x + x^3*Y)
+            sage: L.<y> = K.extension(Y^3 + x + x^3*Y)                                  # needs sage.rings.function_field
             sage: w = y.differential()
             sage: latex(w)
             \left( x y^{2} + \frac{1}{x} y \right)\, dx
@@ -444,7 +444,7 @@ def residue(self, place):
             sage: w = 1/f * f.differential()
             sage: d = f.divisor()
             sage: s = d.support()
-            sage: sum([w.residue(p).trace() for p in s])
+            sage: sum([w.residue(p).trace() for p in s])                                # needs sage.rings.function_field
             0
 
         and in an extension field::
@@ -559,7 +559,7 @@ def cartier(self):
             sage: F.<x> = FunctionField(GF(4))
             sage: f = x/(x^2 + x + 1)
             sage: w = 1/f*f.differential()
-            sage: w.cartier() == w
+            sage: w.cartier() == w                                                      # needs sage.rings.function_field
             True
         """
         W = self.parent()

src/sage/rings/function_field/element.pyx

@@ -569,7 +569,7 @@ 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: 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
             [Place (x, x*y)]
         """

src/sage/rings/function_field/function_field.py

@@ -129,7 +129,7 @@
     sage: TestSuite(L).run(max_runs=8)          # long time (25s)                       # needs sage.rings.function_field sage.rings.number_field
     sage: TestSuite(M).run(max_runs=8)          # long time (35s)                       # needs sage.rings.finite_rings sage.rings.function_field
     sage: TestSuite(N).run(max_runs=8, skip='_test_derivation')         # long time (15s), needs sage.rings.finite_rings
-    sage: TestSuite(O).run()                                                            # needs sage.rings.function_field
+    sage: TestSuite(O).run()
     sage: TestSuite(R).run()                                                            # needs sage.rings.finite_rings sage.rings.function_field
     sage: TestSuite(S).run()                    # long time (4s)                        # needs sage.rings.finite_rings sage.rings.function_field
 

src/sage/rings/function_field/order.py

@@ -30,35 +30,35 @@
 `O` and one maximal infinite order `O_\infty`. There are other non-maximal
 orders such as equation orders::
 
-    sage: # needs sage.rings.finite_rings
+    sage: # needs sage.rings.function_field
     sage: K.<x> = FunctionField(GF(3)); R.<y> = K[]
-    sage: L.<y> = K.extension(y^3 - y - x)                                                          # needs sage.rings.function_field
-    sage: O = L.equation_order()                                                                    # needs sage.rings.function_field
-    sage: 1/y in O                                                                                  # needs sage.rings.function_field
+    sage: L.<y> = K.extension(y^3 - y - x)
+    sage: O = L.equation_order()
+    sage: 1/y in O
     False
-    sage: x/y in O                                                                                  # needs sage.rings.function_field
+    sage: x/y in O
     True
 
 Sage provides an extensive functionality for computations in maximal orders of
 function fields. For example, you can decompose a prime ideal of a rational
 function field in an extension::
 
-    sage: # needs sage.rings.finite_rings
     sage: K.<x> = FunctionField(GF(2)); _.<t> = K[]
     sage: o = K.maximal_order()
     sage: p = o.ideal(x + 1)
-    sage: p.is_prime()
+    sage: p.is_prime()                                                                  # needs sage.libs.pari
     True
 
-    sage: F.<y> = K.extension(t^3 - x^2*(x^2 + x + 1)^2)                                            # needs sage.rings.finite_rings sage.rings.function_field
-    sage: O = F.maximal_order()                                                                     # needs sage.rings.finite_rings sage.rings.function_field
-    sage: O.decomposition(p)                                                                        # needs sage.rings.finite_rings sage.rings.function_field
+    sage: # needs sage.rings.function_field
+    sage: F.<y> = K.extension(t^3 - x^2*(x^2 + x + 1)^2)
+    sage: O = F.maximal_order()
+    sage: O.decomposition(p)
     [(Ideal (x + 1, y + 1) of Maximal order
      of Function field in y defined by y^3 + x^6 + x^4 + x^2, 1, 1),
      (Ideal (x + 1, (1/(x^3 + x^2 + x))*y^2 + y + 1) of Maximal order
      of Function field in y defined by y^3 + x^6 + x^4 + x^2, 2, 1)]
 
-    sage: # needs sage.rings.finite_rings sage.rings.function_field
+    sage: # needs sage.rings.function_field
     sage: p1, relative_degree,ramification_index = O.decomposition(p)[1]
     sage: p1.parent()
     Monoid of ideals of Maximal order of Function field in y
@@ -71,12 +71,12 @@
 When the base constant field is the algebraic field `\QQbar`, the only prime ideals
 of the maximal order of the rational function field are linear polynomials. ::
 
-    sage: # needs sage.rings.number_field
+    sage: # needs sage.rings.function_field sage.rings.number_field
     sage: K.<x> = FunctionField(QQbar)
     sage: R.<y> = K[]
-    sage: L.<y> = K.extension(y^2 - (x^3-x^2))                                                      # needs sage.rings.function_field
+    sage: L.<y> = K.extension(y^2 - (x^3-x^2))
     sage: p = K.maximal_order().ideal(x)
-    sage: L.maximal_order().decomposition(p)                                                        # needs sage.rings.function_field
+    sage: L.maximal_order().decomposition(p)
     [(Ideal (1/x*y - I) of Maximal order of Function field in y defined by y^2 - x^3 + x^2,
       1,
       1),
@@ -274,8 +274,8 @@ def _repr_(self):
             Maximal infinite order of Rational function field in y over Rational Field
 
             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.finite_rings sage.rings.function_field
-            sage: F.maximal_order_infinite()                                                        # needs sage.modules sage.rings.finite_rings sage.rings.function_field
+            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
             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(),)