Trac #23510: Fraction field of fixed modulus p-adic rings should have…

… floating point type

Fraction field of fixed modulus p-adic rings should have floating point
type.

Currently the `change()` method requires that the type be specified, in
this case, but instances such as the check `R.fraction_field() is self`
occurring in _coerce_map_from_(self, R) in padic_extension_generic.pyc.

URL: https://trac.sagemath.org/23510
Reported by: bsinclai
Ticket author(s): David Roe
Reviewer(s): Adele Bourgeois, Julian Rüth

src/doc/en/thematic_tutorials/coercion_and_categories.rst

@@ -1552,6 +1552,7 @@ Here are the tests that form the test suite of quotient fields::
      '_test_elements_eq_transitive',
      '_test_elements_neq',
      '_test_euclidean_degree',
+     '_test_fraction_field',
      '_test_gcd_vs_xgcd',
      '_test_one', '_test_prod',
      '_test_quo_rem',
@@ -1606,6 +1607,7 @@ Let us see what tests are actually performed::
     running ._test_elements_neq() . . . pass
     running ._test_eq() . . . pass
     running ._test_euclidean_degree() . . . pass
+    running ._test_fraction_field() . . . pass
     running ._test_gcd_vs_xgcd() . . . pass
     running ._test_new() . . . pass
     running ._test_not_implemented_methods() . . . pass
@@ -1778,6 +1780,7 @@ interesting.
     running ._test_elements_neq() . . . pass
     running ._test_eq() . . . pass
     running ._test_euclidean_degree() . . . pass
+    running ._test_fraction_field() . . . pass
     running ._test_gcd_vs_xgcd() . . . pass
     running ._test_new() . . . pass
     running ._test_not_implemented_methods() . . . pass

src/sage/categories/integral_domains.py

@@ -107,5 +107,31 @@ def is_integral_domain(self):
             """
             return True
 
+        def _test_fraction_field(self, **options):
+            r"""
+            Test that the fraction field, if it is implemented, works
+            correctly.
+
+            EXAMPLES::
+
+                sage: ZZ._test_fraction_field()
+
+            """
+            tester = self._tester(**options)
+            try:
+                fraction_field = self.fraction_field()
+            except Exception:
+                # some integral domains do not implement fraction_field() yet
+                if self in Fields():
+                    raise
+                return
+
+            for x in tester.some_elements():
+                # check that we can coerce into the fraction field
+                y = fraction_field.coerce(x)
+                # and convert back from it
+                z = self(x)
+                tester.assertEqual(x, z)
+
     class ElementMethods:
         pass

src/sage/rings/padics/CA_template.pxi

@@ -1301,6 +1301,7 @@ cdef class pAdicCoercion_CA_frac_field(RingHomomorphism):
     TESTS::
 
         sage: TestSuite(f).run()
+
     """
     def __init__(self, R, K):
         """

src/sage/rings/padics/CR_template.pxi

@@ -2059,6 +2059,7 @@ cdef class pAdicCoercion_CR_frac_field(RingHomomorphism):
     TESTS::
 
         sage: TestSuite(f).run()
+
     """
     def __init__(self, R, K):
         """