34212: Remove log embedding from number_field_element.pyx

Author: guojing0

src/sage/rings/number_field/number_field_element.pyx

@@ -4118,53 +4118,6 @@ cdef class NumberFieldElement(FieldElement):
         """
         return (self.global_height_non_arch(prec)+self.global_height_arch(prec))/self.number_field().absolute_degree()
 
-    def log_embedding(self, x, prec=53):
-        """
-        Return the logarithmic embedding of ``x``.
-
-        The logarithmic embedding is a tuple of real embeddings and conjugate
-        pairs of compelx embeddings.
-
-        It is defined under Definition 4.9.6 in [Cohen1993]_.
-
-        INPUT:
-
-        - ``x`` -- a rational number.
-        - ``prec`` -- desired floating point precision.
-
-        OUTPUT:
-
-        - a tuple of real numbers.
-
-        EXAMPLES::
-
-            sage: K.<a> = NumberField(x^3 + 5)
-            sage: f = a^2 - 3
-            sage: f.log_embedding(10)
-            (2.30258509299405)
-            sage: f.log_embedding(0)
-            (-1)
-        """
-        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)
-
     def numerator_ideal(self):
         """
         Return the numerator ideal of this number field element.