24464: ZZ is complete

sagemath · Jan 3, 2018 · c0b49bb · c0b49bb
1 parent a178204
commit c0b49bb
Show file tree

Hide file tree

Showing 2 changed files with 6 additions and 7 deletions.
diff --git a/src/doc/en/thematic_tutorials/coercion_and_categories.rst b/src/doc/en/thematic_tutorials/coercion_and_categories.rst
@@ -1300,22 +1300,22 @@ 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
 
 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
@@ -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)