ConvexSet_base._test_contains: Expand and add doctests

src/sage/geometry/convex_set.py

@@ -395,14 +395,61 @@ def contains(self, point):
     def _test_contains(self, tester=None, **options):
         """
         Test the ``contains`` method.
+
+        EXAMPLES::
+
+            sage: from sage.geometry.convex_set import ConvexSet_closed
+            sage: class FaultyConvexSet(ConvexSet_closed):
+            ....:     def ambient_vector_space(self, base_field=QQ):
+            ....:         return base_field^2
+            ....:     ambient = ambient_vector_space
+            ....:     def contains(self, point):
+            ....:         if isinstance(point, (tuple, list)):
+            ....:             return all(x in ZZ for x in point)
+            ....:         return point.parent() == ZZ^2
+            sage: FaultyConvexSet()._test_contains()
+            Traceback (most recent call last):
+            ...
+            AssertionError: False != True
+
+            sage: class AlsoFaultyConvexSet(ConvexSet_closed):
+            ....:     def ambient_vector_space(self, base_field=QQ):
+            ....:         return base_field^2
+            ....:     def ambient(self):
+            ....:         return ZZ^2
+            ....:     def contains(self, point):
+            ....:         return point in ZZ^2
+            sage: AlsoFaultyConvexSet()._test_contains()
+            Traceback (most recent call last):
+            ...
+            AssertionError: True != False
         """
         if tester is None:
             tester = self._tester(**options)
+        ambient = self.ambient()
         space = self.ambient_vector_space()
-        point = space.an_element()
-        coords = space.coordinates(point)
+        try:
+            ambient_point = ambient.an_element()
+        except (AttributeError, NotImplementedError):
+            ambient_point = None
+            space_point = space.an_element()
+        else:
+            space_point = space(ambient_point)
+        space_coords = space.coordinates(space_point)
         if self.contains != NotImplemented:
-            tester.assertEqual(self.contains(point), self.contains(coords))
+            contains_space_point = self.contains(space_point)
+            if ambient_point is not None:
+                tester.assertEqual(contains_space_point, self.contains(ambient_point))
+            tester.assertEqual(contains_space_point, self.contains(space_coords))
+            from sage.rings.qqbar import AA
+            ext_space = self.ambient_vector_space(AA)
+            ext_space_point = ext_space(space_point)
+            tester.assertEqual(contains_space_point, self.contains(ext_space_point))
+            from sage.symbolic.ring import SR
+            symbolic_space = self.ambient_vector_space(SR)
+            symbolic_space_point = symbolic_space(space_point)
+            # Only test that it can accept SR vectors without error.
+            self.contains(symbolic_space_point)
 
     @abstract_method(optional=True)
     def intersection(self, other):