Deprecate is_RelativeNumberField

src/sage/rings/number_field/number_field_element.pyx

@@ -1804,8 +1804,8 @@ cdef class NumberFieldElement(NumberFieldElement_base):
         - Francis Clarke (2010-12-26)
         """
         K = self.parent()
-        from sage.rings.number_field.number_field_rel import is_RelativeNumberField
-        if (not is_RelativeNumberField(L)) or L.base_field() != K:
+        from sage.rings.number_field.number_field_rel import NumberField_relative
+        if not isinstance(L, NumberField_relative) or L.base_field() != K:
             raise ValueError("L (=%s) must be a relative number field with base field K (=%s) in rnfisnorm" % (L, K))
 
         rnf_data = K.pari_rnfnorm_data(L, proof=proof)

src/sage/rings/number_field/number_field_rel.py

@@ -123,6 +123,10 @@ def is_RelativeNumberField(x):
         sage: from sage.rings.number_field.number_field_rel import is_RelativeNumberField
         sage: x = polygen(ZZ, 'x')
         sage: is_RelativeNumberField(NumberField(x^2+1,'a'))
+        doctest:warning...
+        DeprecationWarning: The function is_RelativeNumberField is deprecated;
+        use 'isinstance(..., NumberField_relative)' instead.
+        See https://github.com/sagemath/sage/issues/38124 for details.
         False
         sage: k.<a> = NumberField(x^3 - 2)
         sage: l.<b> = k.extension(x^3 - 3); l
@@ -132,6 +136,10 @@ def is_RelativeNumberField(x):
         sage: is_RelativeNumberField(QQ)
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38124,
+                "The function is_RelativeNumberField is deprecated; "
+                "use 'isinstance(..., NumberField_relative)' instead.")
     return isinstance(x, NumberField_relative)
 
 
@@ -1311,7 +1319,7 @@ def is_isomorphic_relative(self, other, base_isom=None):
             Ring endomorphism of Number Field in z9 with defining polynomial x^6 + x^3 + 1
               Defn: z9 |--> z9^4
         """
-        if is_RelativeNumberField(other):
+        if isinstance(other, NumberField_relative):
             s_base_field = self.base_field()
             o_base_field = other.base_field()
             if base_isom is None:

src/sage/rings/polynomial/polynomial_quotient_ring_element.py

@@ -565,8 +565,8 @@ def field_extension(self, names):
 
         f = R.hom([alpha], F, check=False)
 
-        import sage.rings.number_field.number_field_rel as number_field_rel
-        if number_field_rel.is_RelativeNumberField(F):
+        from sage.rings.number_field.number_field_rel import NumberField_relative
+        if isinstance(F, NumberField_relative):
 
             base_map = F.base_field().hom([R.base_ring().gen()])
             g = F.Hom(R)(x, base_map)