fix

Author: guojing0

src/sage/rings/number_field/number_field.py

@@ -156,7 +156,8 @@
 
 _NumberFields = NumberFields()
 
-
+from sage.categories.homset import Hom
+from sage.categories.sets_cat import Sets
 from sage.rings.number_field.morphism import RelativeNumberFieldHomomorphism_from_abs
 
 
@@ -9328,9 +9329,10 @@ def logarithmic_embedding(self, prec=53):
             sage: f(7)
             (1.94591014905531, 3.89182029811063)
         """
-        log_map = self._NumberFieldElement_logarithmic_embedding_helper(prec)
+        from sage.manifolds.differentiable.examples.euclidean import EuclideanSpace
+        log_map = self(0)._logarithmic_embedding_helper(prec)
         log_hom = Hom(self.base_ring(), EuclideanSpace(len(log_map(0))), Sets())
-        return log_hom(K(0)._NumberFieldElement_logarithmic_embedding_helper)
+        return log_hom(self(0)._logarithmic_embedding_helper)
 
     def places(self, all_complex=False, prec=None):
         r"""

src/sage/rings/number_field/number_field_element.pyx

@@ -86,6 +86,7 @@ ZZ = sage.rings.integer_ring.ZZ
 Integer_sage = sage.rings.integer.Integer
 
 from sage.rings.real_mpfi import RealInterval
+from sage.rings.real_mpfr import RealField
 
 from sage.rings.complex_mpfr import ComplexField
 from sage.rings.cc import CC
@@ -4118,64 +4119,64 @@ cdef class NumberFieldElement(FieldElement):
         return (self.global_height_non_arch(prec)+self.global_height_arch(prec))/self.number_field().absolute_degree()
 
     def _logarithmic_embedding_helper(self, prec=53):
-            """
-            Return the image of ``self`` under the logarithmic embedding.
+        """
+        Return the image of ``self`` under the logarithmic embedding.
 
-            The logarithmic embedding is defined as a map from the number field ``self`` to `\RR^n`.
+        The logarithmic embedding is defined as a map from the number field ``self`` to `\RR^n`.
 
-            It is defined under Definition 4.9.6 in [Cohen1993]_.
+        It is defined under Definition 4.9.6 in [Cohen1993]_.
 
-            INPUT:
+        INPUT:
 
-            - ``prec`` -- desired floating point precision.
+        - ``prec`` -- desired floating point precision.
 
-            OUTPUT:
+        OUTPUT:
 
-            - a tuple of real numbers.
+        - a tuple of real numbers.
 
-            EXAMPLES::
+        EXAMPLES::
 
-                sage: CF.<a> = CyclotomicField(97)
-                sage: log_map = CF._logarithmic_embedding_helper()
-                sage: log_map(0)
-                (-1)
-                sage: log_map(7)
-                (1.94591014905531)
+            sage: CF.<a> = CyclotomicField(97)
+            sage: log_map = CF(0)._logarithmic_embedding_helper()
+            sage: log_map(0)
+            (-1)
+            sage: log_map(7)
+            (1.94591014905531)
 
-            ::
+        ::
 
-                sage: F.<a> = NumberField(x^3 + 5)
-                sage: K.<b> = F.extension(x^2 + 2)
-                sage: log_map = K._logarithmic_embedding_helper()
-                sage: log_map(0)
-                (-1, -1)
-                sage: log_map(7)
-                (1.94591014905531, 3.89182029811063)
+            sage: F.<a> = NumberField(x^3 + 5)
+            sage: K.<b> = F.extension(x^2 + 2)
+            sage: log_map = K(0)._logarithmic_embedding_helper()
+            sage: log_map(0)
+            (-1, -1)
+            sage: log_map(7)
+            (1.94591014905531, 3.89182029811063)
+        """
+        def closure_map(x):
+            """
+            The function closure of the logarithmic embedding.
             """
-            def closure_map(x):
-                """
-                The function closure of the logarithmic embedding.
-                """
-                K = self.base_ring()
-                K_embeddings = K.places(prec)
-                r1, r2 = K.signature()
-                r = r1 + r2 - 1
-
-                Reals = RealField(prec)
-
-                if x == 0:
-                    return vector([-1 for _ in range(r + 1)])
-
-                x_logs = []
-                for i in range(r1):
-                    sigma = K_embeddings[i]
-                    x_logs.append(Reals(abs(sigma(x))).log())
-                for i in range(r1, r + 1):
-                    tau = K_embeddings[i]
-                    x_logs.append(2 * Reals(abs(tau(x))).log())
-
-                return vector(x_logs)
-            return closure_map
+            K = self.base_ring()
+            K_embeddings = K.places(prec)
+            r1, r2 = K.signature()
+            r = r1 + r2 - 1
+
+            Reals = RealField(prec)
+
+            if x == 0:
+                return vector([-1 for _ in range(r + 1)])
+
+            x_logs = []
+            for i in range(r1):
+                sigma = K_embeddings[i]
+                x_logs.append(Reals(abs(sigma(x))).log())
+            for i in range(r1, r + 1):
+                tau = K_embeddings[i]
+                x_logs.append(2 * Reals(abs(tau(x))).log())
+
+            return vector(x_logs)
+        return closure_map
 
     def numerator_ideal(self):
         """