#34537: make number_field_ideal_rel tests more robust

Author: JohnCremona

src/sage/rings/number_field/number_field_ideal_rel.py

@@ -204,8 +204,6 @@ def _from_absolute_ideal(self, id):
         r"""
         Convert the absolute ideal id to a relative number field ideal.
 
-        Assumes id.number_field() == self.absolute_field('a').
-
         WARNING:  This is an internal helper function.
 
         TESTS::
@@ -218,18 +216,18 @@ def _from_absolute_ideal(self, id):
             True
             sage: J.absolute_norm()
             22584817
-            sage: J.absolute_ideal()
-            Fractional ideal (22584817, -1473/812911*a^5 + 8695/4877466*a^4 - 1308209/4877466*a^3 + 117415/443406*a^2 - 22963264/2438733*a - 13721081784272/2438733)
-            sage: J.absolute_ideal().norm()
+            sage: Labs.<c> = L.absolute_field(); Labs # random (polynomial not unique)
+            Number Field in c with defining polynomial x^6 + 217*x^4 - 2*x^3 + 15127*x^2 + 422*x + 338032
+            sage: Jabs = J.absolute_ideal(names='c')
+            sage: Jabs == Labs.ideal(22584817, -1473/812911*c^5 + 8695/4877466*c^4 - 1308209/4877466*c^3 + 117415/443406*c^2 - 22963264/2438733*c - 13721081784272/2438733)
+            True
+            sage: Jabs.norm()
             22584817
-
-            sage: J._from_absolute_ideal(J.absolute_ideal()) == J
+            sage: J._from_absolute_ideal(Jabs) == J
             True
         """
-        L = self.number_field()
-        K = L.absolute_field('a')
-        to_L = K.structure()[0]
-        return L.ideal([to_L(_) for _ in id.gens()])
+        f, _ = id.number_field().structure()
+        return self.number_field().ideal([f(_) for _ in id.gens()])
 
     def free_module(self):
         r"""