34212: Correct doc and add an example

Author: guojing0

src/sage/rings/number_field/number_field.py

@@ -9309,7 +9309,7 @@ def logarithmic_embedding(self, prec=53):
 
         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 [Coh1993]_.
 
         INPUT:
 
@@ -9336,6 +9336,15 @@ def logarithmic_embedding(self, prec=53):
             (-1, -1)
             sage: f(7)
             (1.94591014905531, 3.89182029811063)
+
+        ::
+
+            sage: K.<a> = NumberField(x^4 - 8*x^2 + 3)
+            sage: f = logarithmic_embedding(K)
+            sage: f(0)
+            (-1, -1, -1, -1)
+            sage: f(7)
+            (3.89182029811063, 3.89182029811063, 3.89182029811063, 3.89182029811063)
         """
         def closure_map(x, prec=53):
             """