From c0b49bb8016703be8e530686c0acae4b78412a86 Mon Sep 17 00:00:00 2001
From: Vincent Delecroix <20100.delecroix@gmail.com>
Date: Wed, 3 Jan 2018 17:06:56 +0100
Subject: [PATCH] 24464: ZZ is complete

---
 src/doc/en/thematic_tutorials/coercion_and_categories.rst | 6 +++---
 src/sage/rings/integer_ring.pyx                           | 7 +++----
 2 files changed, 6 insertions(+), 7 deletions(-)

diff --git a/src/doc/en/thematic_tutorials/coercion_and_categories.rst b/src/doc/en/thematic_tutorials/coercion_and_categories.rst
index e1e1872a5fe..a01f1acee33 100644
--- a/src/doc/en/thematic_tutorials/coercion_and_categories.rst
+++ b/src/doc/en/thematic_tutorials/coercion_and_categories.rst
@@ -1300,7 +1300,7 @@ When we apply ``Compl``, ``Matr`` and ``Poly`` to the ring of integers, we
 obtain::
 
     sage: (Poly*Matr*Compl)(ZZ)
-    Univariate Polynomial Ring in x over Full MatrixSpace of 3 by 3 dense matrices over Real Field with 53 bits of precision
+    Univariate Polynomial Ring in x over Full MatrixSpace of 3 by 3 dense matrices over Integer Ring
 
 .. end of output
 
@@ -1308,14 +1308,14 @@ Applying the shuffling procedure yields
 ::
 
     sage: (Poly*Matr*Fract*Poly*AlgClos*Fract*Compl)(ZZ)
-    Univariate Polynomial Ring in x over Full MatrixSpace of 3 by 3 dense matrices over Fraction Field of Univariate Polynomial Ring in x over Complex Field with 53 bits of precision
+    Univariate Polynomial Ring in x over Full MatrixSpace of 3 by 3 dense matrices over Fraction Field of Univariate Polynomial Ring in x over Algebraic Field
 
 .. end of output
 
 and this is indeed equal to the pushout found by Sage::
 
     sage: pushout((Fract*Poly*AlgClos*Fract)(ZZ), (Poly*Matr*Compl)(ZZ))
-    Univariate Polynomial Ring in x over Full MatrixSpace of 3 by 3 dense matrices over Fraction Field of Univariate Polynomial Ring in x over Complex Field with 53 bits of precision
+    Univariate Polynomial Ring in x over Full MatrixSpace of 3 by 3 dense matrices over Fraction Field of Univariate Polynomial Ring in x over Algebraic Field
 
 .. end of output
 
diff --git a/src/sage/rings/integer_ring.pyx b/src/sage/rings/integer_ring.pyx
index 3425989aac6..6fcb4f77cb1 100644
--- a/src/sage/rings/integer_ring.pyx
+++ b/src/sage/rings/integer_ring.pyx
@@ -1106,7 +1106,7 @@ cdef class IntegerRing_class(PrincipalIdealDomain):
 
     def completion(self, p, prec, extras = {}):
         r"""
-        Return the completion of the integers at the prime `p`.
+        Return the metric completion of the integers at the prime `p`.
 
         INPUT:
 
@@ -1124,13 +1124,12 @@ cdef class IntegerRing_class(PrincipalIdealDomain):
         EXAMPLES::
 
             sage: ZZ.completion(infinity, 53)
-            Real Field with 53 bits of precision
+            Integer Ring
             sage: ZZ.completion(5, 15, {'print_mode': 'bars'})
             5-adic Ring with capped relative precision 15
         """
         if p == sage.rings.infinity.Infinity:
-            from sage.rings.real_mpfr import create_RealField
-            return create_RealField(prec, **extras)
+            return self
         else:
             from sage.rings.padics.factory import Zp
             return Zp(p, prec, **extras)