sage.rings.number_field: Fix up replacement of is_{Real,Complex}[Doub…

…le]Field

src/sage/rings/number_field/number_field.py

@@ -9945,16 +9945,14 @@ def hilbert_symbol(self, a, b, P = None):
             if P.domain() is not self:
                 raise ValueError("Domain of P (=%s) should be self (=%s) in self.hilbert_symbol" % (P, self))
             codom = P.codomain()
-            from sage.rings.complex_mpfr import is_ComplexField
             from sage.rings.complex_interval_field import is_ComplexIntervalField
-            from sage.rings.real_mpfr import is_RealField
-            from sage.rings.all import (AA, CDF, QQbar, RDF)
-            if isinstance(codom, sage.rings.abc.ComplexField) or is_ComplexIntervalField(codom) or \
-                                         codom is CDF or codom is QQbar:
+            from sage.rings.all import (AA, QQbar)
+            if isinstance(codom, (sage.rings.abc.ComplexField, sage.rings.abc.ComplexDoubleField) or is_ComplexIntervalField(codom) or \
+                                         codom is QQbar:
                 if P(self.gen()).imag() == 0:
                     raise ValueError("Possibly real place (=%s) given as complex embedding in hilbert_symbol. Is it real or complex?" % P)
                 return 1
-            if isinstance(codom, sage.rings.abc.RealField) or codom is RDF or codom is AA:
+            if isinstance(codom, (sage.rings.abc.RealField, sage.rings.abc.RealDoubleField) or codom is AA:
                 if P(a) > 0 or P(b) > 0:
                     return 1
                 return -1
@@ -12317,7 +12315,7 @@ def refine_embedding(e, prec=None):
         return e
 
     # We first compute all the embeddings at the new precision:
-    if sage.rings.real_mpfr.isinstance(RC, sage.rings.abc.RealField) or RC in (RDF, RLF):
+    if isinstance(RC, (sage.rings.abc.RealField, sage.rings.abc.RealDoubleField)) or RC == RLF:
         if prec == Infinity:
             elist = K.embeddings(sage.rings.qqbar.AA)
         else: