Make Qp.integer_ring() faster.

src/sage/rings/padics/generic_nodes.py

@@ -1423,13 +1423,19 @@ def construction(self, forbid_frac_field=False):
             sage: S = F(Z)
             sage: S._precision_cap()
             (31, 41)
+
+        The `secure` attribute for relaxed type is included in the functor::
+
+            sage: R = ZpER(5, secure=True)
+            sage: R.construction()
+            (Completion[5, prec=(20, 40, True)], Integer Ring)
         """
         from sage.categories.pushout import CompletionFunctor
         extras = {'print_mode':self._printer.dict(), 'type':self._prec_type(), 'names':self._names}
         if hasattr(self, '_label'):
             extras['label'] = self._label
         if self._prec_type() == "relaxed":
-            prec = (self._default_prec, self._halting_prec)
+            prec = (self._default_prec, self._halting_prec, self._secure)
         else:
             prec = self._precision_cap()
         return (CompletionFunctor(self.prime(), prec, extras), ZZ)
@@ -1595,14 +1601,20 @@ def construction(self, forbid_frac_field=False):
             sage: S = F(Z)
             sage: S._precision_cap()
             (31, 41)
+
+        The `secure` attribute for relaxed type is included in the functor::
+
+            sage: K = QpER(5, secure=True)
+            sage: K.construction(forbid_frac_field=True)
+            (Completion[5, prec=(20, 40, True)], Rational Field)
         """
         from sage.categories.pushout import FractionField, CompletionFunctor
         if forbid_frac_field:
             extras = {'print_mode':self._printer.dict(), 'type':self._prec_type(), 'names':self._names}
             if hasattr(self, '_label'):
                 extras['label'] = self._label
             if self._prec_type() == "relaxed":
-                prec = (self._default_prec, self._halting_prec)
+                prec = (self._default_prec, self._halting_prec, self._secure)
             else:
                 prec = self._precision_cap()
             return (CompletionFunctor(self.prime(), prec, extras), QQ)

src/sage/rings/padics/local_generic.py

@@ -375,6 +375,25 @@ def change(self, **kwds):
             37-adic Ring with lattice-cap precision (label: change)
             sage: S.change(label = "new")
             37-adic Ring with lattice-cap precision (label: new)
+
+
+        TESTS:
+
+        The `secure` attribute for relaxed type is copied::
+
+            sage: R = ZpER(5, secure=True); R
+            5-adic Ring handled with relaxed arithmetics
+            sage: K = R.change(field=True); K
+            5-adic Field handled with relaxed arithmetics
+            sage: K.is_secure()
+            True
+
+        The `check=False` option works for relaxed type::
+
+            sage: R = ZpER(5) ; R
+            5-adic Ring handled with relaxed arithmetics
+            sage: K = R.change(field=True, check=False) ; K
+            5-adic Field handled with relaxed arithmetics
         """
         # We support both print_* and * for *=mode, pos, sep, alphabet
         for atr in ('print_mode', 'print_pos', 'print_sep', 'print_alphabet'):

src/sage/rings/padics/padic_base_leaves.py

@@ -1128,6 +1128,8 @@ def __init__(self, p, prec, print_mode, names):
 
             sage: R = ZpER(7)
             sage: TestSuite(R).run(skip=['_test_log', '_test_matrix_smith'])
+            sage: R = ZpER(7, secure=True)
+            sage: TestSuite(R).run(skip=['_test_log', '_test_matrix_smith'])
         """
         from sage.rings.padics import padic_relaxed_element
         self._default_prec, self._halting_prec, self._secure = prec
@@ -1163,6 +1165,8 @@ def __init__(self, p, prec, print_mode, names):
 
             sage: K = QpER(7)
             sage: TestSuite(K).run(skip=['_test_log', '_test_matrix_smith'])
+            sage: K = QpER(7, secure=True)
+            sage: TestSuite(K).run(skip=['_test_log', '_test_matrix_smith'])
         """
         from sage.rings.padics import padic_relaxed_element
         self._default_prec, self._halting_prec, self._secure = prec

src/sage/rings/padics/padic_generic.py

@@ -478,14 +478,20 @@ def integer_ring(self, print_mode=None):
             2-adic Ring with lattice-cap precision (label: test)
             sage: R.integer_ring({'mode':'series'}) is R
             True
+
+        The `secure` attribute for relaxed type is preserved::
+
+            sage: K = QpER(5, secure=True)
+            sage: K.integer_ring().is_secure()
+            True
         """
         # Currently does not support fields with non integral defining
         # polynomials.  This should change when the padic_general_extension
         # framework gets worked out.
         if not self.is_field() and print_mode is None:
             return self
         if print_mode is None:
-            return self.change(field=False)
+            return self.change(field=False, check=False)
         else:
             from sage.misc.superseded import deprecation
             deprecation(23227, "Use the change method if you want to change print options in integer_ring()")