moving fraction_field method to categories

Author: fchapoton

src/doc/en/thematic_tutorials/coercion_and_categories.rst

@@ -104,8 +104,7 @@ it makes sense to build on top of the base class
 This base class provides a lot more methods than a general parent::
 
     sage: [p for p in dir(Field) if p not in dir(Parent)]
-    ['_CommutativeRing__fraction_field',
-     '__iter__',
+    ['__iter__',
      '__len__',
      '__rxor__',
      '__xor__',
@@ -124,7 +123,6 @@ This base class provides a lot more methods than a general parent::
      'base_extend',
      'epsilon',
      'extension',
-     'fraction_field',
      'gen',
      'gens',
      'ngens',

src/sage/categories/commutative_rings.py

@@ -14,6 +14,7 @@
 
 from sage.categories.category_with_axiom import CategoryWithAxiom
 from sage.categories.cartesian_product import CartesianProductsCategory
+from sage.misc.cachefunc import cached_method
 from sage.structure.sequence import Sequence
 
 
@@ -539,6 +540,30 @@ def derivation(self, arg=None, twist=None):
                 codomain = self
             return self.derivation_module(codomain, twist=twist)(arg)
 
+        @cached_method
+        def fraction_field(self):
+            """
+            Return the fraction field of ``self``.
+
+            EXAMPLES::
+
+                sage: R = Integers(389)['x,y']
+                sage: Frac(R)
+                Fraction Field of Multivariate Polynomial Ring in x, y over Ring of integers modulo 389
+                sage: R.fraction_field()
+                Fraction Field of Multivariate Polynomial Ring in x, y over Ring of integers modulo 389
+            """
+            # from sage.categories.fields import Fields
+            from sage.categories.integral_domains import IntegralDomains
+            if self.is_field():  # self in Fields():
+                return self
+            if self not in IntegralDomains():
+                raise TypeError("self must be an integral domain")
+
+            import sage.rings.fraction_field
+            return sage.rings.fraction_field.FractionField_generic(self)
+
+
     class ElementMethods:
         pass
 

src/sage/categories/integral_domains.py

@@ -30,7 +30,7 @@
 #  Distributed under the terms of the GNU General Public License (GPL)
 #                  https://www.gnu.org/licenses/
 # *****************************************************************************
-
+from sage.misc.cachefunc import cached_method
 from sage.misc.lazy_import import lazy_import
 from sage.misc.lazy_attribute import lazy_class_attribute
 from sage.categories.category_with_axiom import CategoryWithAxiom
@@ -174,6 +174,22 @@ def localization(self, additional_units, names=None, normalize=True, category=No
             from sage.rings.localization import Localization
             return Localization(self, additional_units, names=names, normalize=normalize, category=category)
 
+        @cached_method
+        def fraction_field(self):
+            """
+            Return the fraction field of ``self``.
+
+            EXAMPLES::
+
+                sage: R = GF(61)['x,y']
+                sage: Frac(R)
+                Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 61
+                sage: R.fraction_field()
+                Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 61
+            """
+            import sage.rings.fraction_field
+            return sage.rings.fraction_field.FractionField_generic(self)
+
         def _test_fraction_field(self, **options):
             r"""
             Test that the fraction field, if it is implemented, works
@@ -184,14 +200,7 @@ def _test_fraction_field(self, **options):
                 sage: ZZ._test_fraction_field()
             """
             tester = self._tester(**options)
-            try:
-                fraction_field = self.fraction_field()
-            except (AttributeError, ImportError):
-                # some integral domains do not implement fraction_field() yet
-                if self in Fields():
-                    raise
-                return
-
+            fraction_field = self.fraction_field()
             for x in tester.some_elements():
                 # check that we can coerce into the fraction field
                 fraction_field.coerce(x)

src/sage/categories/rings.py

@@ -400,7 +400,7 @@ def is_integral_domain(self, proof=True) -> bool:
                 sage: R.fraction_field()                                                    # needs sage.libs.pari
                 Traceback (most recent call last):
                 ...
-                TypeError: self must be an integral domain.
+                TypeError: self must be an integral domain
                 sage: R.is_integral_domain()                                                # needs sage.libs.pari
                 False
 

src/sage/rings/finite_rings/integer_mod_ring.py

@@ -791,7 +791,7 @@ def _pseudo_fraction_field(self):
             sage: Integers(15).fraction_field()
             Traceback (most recent call last):
             ...
-            TypeError: self must be an integral domain.
+            TypeError: self must be an integral domain
             sage: Integers(15)._pseudo_fraction_field()
             Ring of integers modulo 15
             sage: R.<x> = Integers(15)[]

src/sage/rings/lazy_series_ring.py

@@ -4120,6 +4120,20 @@ def _an_element_(self):
         c = self.base_ring().an_element()
         return self.element_class(self, Stream_exact([], constant=c, order=4))
 
+    def ngens(self):
+        r"""
+        Return the number of generators of ``self``.
+
+        This is always 1.
+
+        EXAMPLES::
+
+            sage: L = LazyDirichletSeriesRing(ZZ, 'z')
+            sage: L.ngens()
+            1
+        """
+        return 1
+
     def some_elements(self):
         """
         Return a list of elements of ``self``.

src/sage/rings/padics/padic_valuation.py

@@ -1397,26 +1397,17 @@ def _fraction_field(ring):
     r"""
     Return a fraction field of ``ring``.
 
-    EXAMPLES:
+    This workaround is no longer needed.
 
-    This works around some annoyances with ``ring.fraction_field()``::
+    EXAMPLES::
 
         sage: R.<x> = ZZ[]
         sage: S = R.quo(x^2 + 1)
         sage: S.fraction_field()
-        Fraction Field of Univariate Quotient Polynomial Ring in xbar over Integer Ring with modulus x^2 + 1
+        Univariate Quotient Polynomial Ring in xbar over Rational Field with modulus x^2 + 1
 
         sage: from sage.rings.padics.padic_valuation import _fraction_field
         sage: _fraction_field(S)
         Univariate Quotient Polynomial Ring in xbar over Rational Field with modulus x^2 + 1
     """
-    from sage.categories.fields import Fields
-    if ring in Fields():
-        return ring
-
-    from sage.rings.polynomial.polynomial_quotient_ring import PolynomialQuotientRing_generic
-    if isinstance(ring, PolynomialQuotientRing_generic):
-        from sage.categories.integral_domains import IntegralDomains
-        if ring in IntegralDomains():
-            return ring.base().change_ring(ring.base_ring().fraction_field()).quo(ring.modulus())
     return ring.fraction_field()

src/sage/rings/polynomial/multi_polynomial_ideal.py

@@ -4914,7 +4914,7 @@ def subs(self, in_dict=None, **kwds):
             sage: var("z")                                                              # needs sage.symbolic
             z
             sage: I.subs(a=z, b=z)                                                      # needs sage.symbolic
-            Principal ideal (2*z^2 + 2) of Symbolic Ring
+            Principal ideal (1) of Symbolic Ring
 
         Variables that are not substituted remain unchanged::
 

src/sage/rings/polynomial/multi_polynomial_libsingular.pyx

@@ -2318,12 +2318,12 @@ cdef class MPolynomial_libsingular(MPolynomial_libsingular_base):
             sage: x/P(3)
             Traceback (most recent call last):
             ...
-            TypeError: self must be an integral domain.
+            TypeError: self must be an integral domain
 
             sage: x/3
             Traceback (most recent call last):
             ...
-            TypeError: self must be an integral domain.
+            TypeError: self must be an integral domain
 
         TESTS::
 

src/sage/rings/polynomial/polynomial_quotient_ring.py

@@ -1254,6 +1254,27 @@ def polynomial_ring(self):
 
     cover_ring = polynomial_ring
 
+    def fraction_field(self):
+        """
+        Return the fraction field of ``self``.
+
+        EXAMPLES::
+
+            sage: R.<x> = ZZ[]
+            sage: S = R.quo(x^2 + 1)
+            sage: S.fraction_field()
+            Univariate Quotient Polynomial Ring in xbar over Rational Field with modulus x^2 + 1
+        """
+        from sage.categories.fields import Fields
+        from sage.categories.integral_domains import IntegralDomains
+        if self in Fields():
+            return self
+        if self not in IntegralDomains():
+            raise TypeError("self must be an integral domain")
+
+        frac = self.base_ring().fraction_field()
+        return self.base().change_ring(frac).quo(self.modulus())
+
     def random_element(self, degree=None, *args, **kwds):
         """
         Return a random element of this quotient ring.