moving fraction_field method to categories

src/doc/en/thematic_tutorials/coercion_and_categories.rst

@@ -105,8 +105,7 @@ Let us nevertheless provide an example using::
 as this base class still provides a few 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__',
@@ -121,7 +120,6 @@ as this base class still provides a few more methods than a general parent::
      '_zero_element',
      'base_extend',
      'extension',
-     'fraction_field',
      'gen',
      'gens',
      'ngens',

src/sage/algebras/splitting_algebra.py

@@ -40,6 +40,7 @@
 from sage.misc.cachefunc import cached_method
 from sage.rings.polynomial.polynomial_quotient_ring import PolynomialQuotientRing_domain
 from sage.rings.polynomial.polynomial_quotient_ring_element import PolynomialQuotientRingElement
+from sage.structure.category_object import normalize_names
 
 
 # -------------------------------------------------------------------------
@@ -221,12 +222,11 @@
         # checking input parameters
         # ---------------------------------------------------------------
 
-        base_ring = monic_polynomial.base_ring()
         if not monic_polynomial.is_monic():
             raise ValueError("given polynomial must be monic")
         deg = monic_polynomial.degree()
 
-        from sage.structure.category_object import normalize_names
+        base_ring = monic_polynomial.base_ring()
         self._root_names = normalize_names(deg - 1, names)
         root_names = list(self._root_names)
         verbose("Create splitting algebra to base ring %s and polynomial %s (%s %s)"
@@ -374,7 +374,6 @@
             invert_items = list(self._invertible_elements.items())
             for k, v in invert_items:
                 self._invertible_elements.update({v: k})
-        return
 
     ########################################################################
     # ----------------------------------------------------------------------
@@ -400,7 +399,7 @@
             False,
             False))
 
             sage: TestSuite(S).run()
         """
         def_polynomial = self.defining_polynomial()
         def_coefficients = self._coefficients_list[0]
@@ -475,7 +474,7 @@
             u + v
             sage: S(X*Y + X)
             X*Y + X
             sage: TestSuite(S).run()                   # indirect doctest
         """
         if isinstance(x, SplittingAlgebraElement):
             # coercion from covering fixes pickling problems

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
 from sage.structure.element import coercion_model
 
@@ -561,7 +562,7 @@ 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
 
             TESTS::
 
@@ -575,6 +576,33 @@ def _pseudo_fraction_field(self):
             except (NotImplementedError, TypeError):
                 return coercion_model.division_parent(self)
 
+        @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
+            try:
+                if self.is_field():
+                    # self in Fields(): would turn SR into a field !
+                    return self
+            except NotImplementedError:
+                pass
+            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:
         def is_square(self, root=False):
             """

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

@@ -398,7 +398,7 @@ 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/combinat/sf/sf.py

@@ -863,7 +863,7 @@ def __init__(self, R):
 
             sage: Sym1 = SymmetricFunctions(FiniteField(23))
             sage: Sym2 = SymmetricFunctions(Integers(23))
-            sage: TestSuite(Sym).run()
+            sage: TestSuite(Sym).run(skip="_test_fraction_field")
         """
         # change the line below to assert(R in Rings()) once MRO issues from #15536, #15475 are resolved
         assert R in Fields() or R in Rings()  # side effect of this statement assures MRO exists for R

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

@@ -2754,7 +2754,7 @@
             sage: L = LazyPowerSeriesRing(Zmod(6), 't')
             sage: TestSuite(L).run(skip=['_test_revert'])
             sage: L = LazyPowerSeriesRing(Zmod(6), 's, t')
             sage: TestSuite(L).run(skip=['_test_revert'])
 
             sage: L = LazyPowerSeriesRing(QQ['q'], 't')
             sage: TestSuite(L).run(skip='_test_fraction_field')
@@ -4194,6 +4194,20 @@
         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

@@ -1406,26 +1406,17 @@ 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_libsingular.pyx

@@ -2320,12 +2320,12 @@ 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

@@ -171,7 +171,7 @@ class PolynomialQuotientRingFactory(UniqueFactory):
         sage: R.quotient_by_principal_ideal(f)
         Univariate Quotient Polynomial Ring in xbar over Rational Field with modulus x^2 - 1
     """
-    def create_key(self, ring, polynomial, names=None):
+    def create_key(self, ring, polynomial, names=None, category=None):
         r"""
         Return a unique description of the quotient ring specified by the
         arguments.
@@ -180,15 +180,15 @@ def create_key(self, ring, polynomial, names=None):
 
             sage: R.<x> = QQ[]
             sage: PolynomialQuotientRing.create_key(R, x + 1)
-            (Univariate Polynomial Ring in x over Rational Field, x + 1, ('xbar',))
+            (Univariate Polynomial Ring in x over Rational Field, x + 1, ('xbar',), None)
 
         TESTS:
 
         We do not normalize the modulus even though we could divide out the
         leading coefficient here::
 
             sage: PolynomialQuotientRing.create_key(R, 2*x + 2)
-            (Univariate Polynomial Ring in x over Rational Field, 2*x + 2, ('xbar',))
+            (Univariate Polynomial Ring in x over Rational Field, 2*x + 2, ('xbar',), None)
 
         Consequently, you get two distinct objects::
 
@@ -223,7 +223,7 @@ def create_key(self, ring, polynomial, names=None):
         else:
             names = normalize_names(ring.ngens(), names)
 
-        return ring, polynomial, names
+        return ring, polynomial, names, category
 
     def create_object(self, version, key):
         r"""
@@ -233,26 +233,26 @@ def create_object(self, version, key):
 
             sage: R.<x> = QQ[]
             sage: PolynomialQuotientRing.create_object((8, 0, 0),
-            ....:                                      (R, x^2 - 1, ('xbar')))
+            ....:                                      (R, x^2 - 1, ('xbar'), None))
             Univariate Quotient Polynomial Ring in xbar over Rational Field with modulus x^2 - 1
         """
-        ring, polynomial, names = key
+        ring, polynomial, names, category = key
 
         R = ring.base_ring()
         from sage.categories.fields import Fields
         from sage.categories.integral_domains import IntegralDomains
         if R in IntegralDomains():
             try:
                 is_irreducible = polynomial.is_irreducible()
-            except NotImplementedError: # is_irreducible sometimes not implemented
+            except NotImplementedError:  # is_irreducible sometimes not implemented
                 pass
             else:
                 if is_irreducible:
                     if R in Fields():
-                        return PolynomialQuotientRing_field(ring, polynomial, names)
+                        return PolynomialQuotientRing_field(ring, polynomial, names, category=category)
                     else:
-                        return PolynomialQuotientRing_domain(ring, polynomial, names)
-        return PolynomialQuotientRing_generic(ring, polynomial, names)
+                        return PolynomialQuotientRing_domain(ring, polynomial, names, category=category)
+        return PolynomialQuotientRing_generic(ring, polynomial, names, category=category)
 
 
 PolynomialQuotientRing = PolynomialQuotientRingFactory("PolynomialQuotientRing")
@@ -434,14 +434,16 @@ def __init__(self, ring, polynomial, name=None, category=None):
 
         self.__ring = ring
         self.__polynomial = polynomial
-        category = CommutativeAlgebras(ring.base_ring().category()).Quotients().or_subcategory(category)
+        cat = CommutativeAlgebras(ring.base_ring().category()).Quotients()
+        if category is not None:
+            cat &= category
         if self.is_finite():
             # We refine the category for finite quotients.
             # Note that is_finite() is cheap so it does not seem to do a lazy
             # _refine_category_() in is_finite() as we do for is_field()
-            category = category.Finite()
+            cat = cat.Finite()
 
-        QuotientRing_generic.__init__(self, ring, ring.ideal(polynomial), names=name, category=category)
+        QuotientRing_generic.__init__(self, ring, ring.ideal(polynomial), names=name, category=cat)
         self._base = ring  # backwards compatibility -- different from QuotientRing_generic
 
     _ideal_class_ = QuotientRing_generic._ideal_class_
@@ -532,9 +534,9 @@ def _element_constructor_(self, x):
         """
         if not isinstance(x, str):
             try:
-                return self.element_class(self, self.__ring(x) , check=True)
-            except TypeError:
-                xlift = getattr(x,'lift',None)
+                return self.element_class(self, self.__ring(x), check=True)
+            except (TypeError, ValueError):
+                xlift = getattr(x, 'lift', None)
                 if xlift is not None: # duck typing for quotient ring elements
                     return self.element_class(self, self.__ring(x.lift()), check=False)
         # The problem with the string representation is that it could in principle
@@ -595,7 +597,7 @@ def _coerce_map_from_(self, R):
             try:
                 if not self.__polynomial.divides(R.modulus()):
                     return False
-            except (ZeroDivisionError,ArithmeticError):
+            except (ZeroDivisionError, ArithmeticError):
                 return False
             from sage.categories.homset import Hom
             parent = Hom(R, self, category=self.category()._meet_(R.category()))
@@ -1259,6 +1261,28 @@ 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(),
+                                                 category=Fields())
+
     def random_element(self, degree=None, *args, **kwds):
         """
         Return a random element of this quotient ring.
@@ -2317,8 +2341,10 @@ def __init__(self, ring, polynomial, name=None, category=None):
             sage: h.parent() is H
             True
         """
-        category = CommutativeAlgebras(ring.base_ring().category()).Quotients().NoZeroDivisors().or_subcategory(category)
-        PolynomialQuotientRing_generic.__init__(self, ring, polynomial, name, category)
+        cat = CommutativeAlgebras(ring.base_ring().category()).Quotients().NoZeroDivisors()
+        if category is not None:
+            cat &= category
+        PolynomialQuotientRing_generic.__init__(self, ring, polynomial, name, cat)
 
     def field_extension(self, names):
         r"""