make a category of Dedekind domains, remove code from ring.pyx

src/sage/categories/all.py

@@ -81,7 +81,7 @@
 RingModules = Modules
 from sage.categories.vector_spaces import VectorSpaces
 
-# (hopf) algebra structures
+# (Hopf) algebra structures
 from sage.categories.algebras import Algebras
 from sage.categories.commutative_algebras import CommutativeAlgebras
 from sage.categories.coalgebras import Coalgebras

src/sage/categories/basic.py

@@ -42,6 +42,7 @@
 from sage.categories.commutative_rings import CommutativeRings
 from sage.categories.integral_domains import IntegralDomains
 from sage.categories.gcd_domains import GcdDomains
+from sage.categories.dedekind_domains import DedekindDomains
 from sage.categories.principal_ideal_domains import PrincipalIdealDomains
 from sage.categories.euclidean_domains import EuclideanDomains
 from sage.categories.unique_factorization_domains import UniqueFactorizationDomains

src/sage/categories/category.py

@@ -119,7 +119,7 @@
 _join_cache = WeakValueDictionary()
 
 
-HALL_OF_FAME = ['Coxeter', 'Hopf', 'Weyl', 'Lie', 'Hecke']
+HALL_OF_FAME = ['Coxeter', 'Hopf', 'Weyl', 'Lie', 'Hecke', 'Dedekind']
 
 
 class Category(UniqueRepresentation, SageObject):
@@ -2592,6 +2592,7 @@ def category_sample():
         sage: from sage.categories.category import category_sample
         sage: sorted(category_sample(), key=str)                                        # needs sage.groups
         [Category of Coxeter groups,
+         Category of Dedekind domains,
          Category of G-sets for Symmetric group of order 8! as a permutation group,
          Category of Hecke modules over Rational Field,
          Category of Hopf algebras over Rational Field,

src/sage/categories/dedekind_domains.py

@@ -0,0 +1,155 @@
+r"""
+Dedekind Domains
+"""
+# ****************************************************************************
+#  Distributed under the terms of the GNU General Public License (GPL)
+#                  https://www.gnu.org/licenses/
+# *****************************************************************************
+from sage.categories.category import Category
+from sage.categories.integral_domains import IntegralDomains
+
+
+class DedekindDomains(Category):
+    """
+    The category of Dedekind domains.
+
+    A Dedekind domain is a Noetherian integral domain of Krull
+    dimension one that is integrally closed in its field of fractions.
+
+    EXAMPLES::
+
+        sage: C = DedekindDomains(); C
+        Category of Dedekind domains
+        sage: C.super_categories()
+        [Category of integral domains]
+
+    TESTS::
+
+        sage: TestSuite(C).run()
+    """
+    def super_categories(self):
+        """
+        EXAMPLES::
+
+            sage: DedekindDomains().super_categories()
+            [Category of integral domains]
+        """
+        return [IntegralDomains()]
+
+    class ParentMethods:
+        def krull_dimension(self):
+            """
+            Return 1 since Dedekind domains have Krull dimension 1.
+
+            EXAMPLES:
+
+            The following are examples of Dedekind domains::
+
+                sage: ZZ.krull_dimension()
+                1
+                sage: x = polygen(ZZ, 'x')
+                sage: K = NumberField(x^2 + 1, 's')                                         # needs sage.rings.number_field
+                sage: OK = K.ring_of_integers()                                             # needs sage.rings.number_field
+                sage: OK.krull_dimension()                                                  # needs sage.rings.number_field
+                1
+
+            The following are not Dedekind domains but have
+            a ``krull_dimension`` function::
+
+                sage: QQ.krull_dimension()
+                0
+                sage: T.<x,y> = PolynomialRing(QQ,2); T
+                Multivariate Polynomial Ring in x, y over Rational Field
+                sage: T.krull_dimension()
+                2
+                sage: U.<x,y,z> = PolynomialRing(ZZ,3); U
+                Multivariate Polynomial Ring in x, y, z over Integer Ring
+                sage: U.krull_dimension()
+                4
+
+                sage: # needs sage.rings.number_field
+                sage: K.<i> = QuadraticField(-1)
+                sage: R = K.order(2*i); R
+                Order of conductor 2 generated by 2*i
+                 in Number Field in i with defining polynomial x^2 + 1 with i = 1*I
+                sage: R.is_maximal()
+                False
+                sage: R.krull_dimension()
+                1
+            """
+            from sage.rings.integer_ring import ZZ
+            return ZZ.one()
+
+        def is_integrally_closed(self) -> bool:
+            """
+            Return ``True`` since Dedekind domains are integrally closed.
+
+            EXAMPLES:
+
+            The following are examples of Dedekind domains::
+
+                sage: ZZ.is_integrally_closed()
+                True
+                sage: x = polygen(ZZ, 'x')
+                sage: K = NumberField(x^2 + 1, 's')                                         # needs sage.rings.number_field
+                sage: OK = K.ring_of_integers()                                             # needs sage.rings.number_field
+                sage: OK.is_integrally_closed()                                             # needs sage.rings.number_field
+                True
+
+            These, however, are not Dedekind domains::
+
+                sage: QQ.is_integrally_closed()
+                True
+                sage: S = ZZ[sqrt(5)]; S.is_integrally_closed()                             # needs sage.rings.number_field sage.symbolic
+                False
+                sage: T.<x,y> = PolynomialRing(QQ, 2); T
+                Multivariate Polynomial Ring in x, y over Rational Field
+                sage: T.is_integral_domain()
+                True
+            """
+            return True
+
+        def integral_closure(self):
+            r"""
+            Return ``self`` since Dedekind domains are integrally closed.
+
+            EXAMPLES::
+
+                sage: # needs sage.rings.number_field
+                sage: x = polygen(ZZ, 'x')
+                sage: K = NumberField(x^2 + 1, 's')
+                sage: OK = K.ring_of_integers()
+                sage: OK.integral_closure()
+                Gaussian Integers generated by s in Number Field in s
+                 with defining polynomial x^2 + 1
+                sage: OK.integral_closure() == OK
+                True
+
+                sage: QQ.integral_closure() == QQ
+                True
+            """
+            return self
+
+        def is_noetherian(self) -> bool:
+            r"""
+            Return ``True`` since Dedekind domains are Noetherian.
+
+            EXAMPLES:
+
+            The integers, `\ZZ`, and rings of integers of number
+            fields are Dedekind domains::
+
+                sage: ZZ.is_noetherian()
+                True
+                sage: x = polygen(ZZ, 'x')
+                sage: K = NumberField(x^2 + 1, 's')                                         # needs sage.rings.number_field
+                sage: OK = K.ring_of_integers()                                             # needs sage.rings.number_field
+                sage: OK.is_noetherian()                                                    # needs sage.rings.number_field
+                True
+                sage: QQ.is_noetherian()
+                True
+            """
+            return True
+
+    class ElementMethods:
+        pass

src/sage/rings/integer_ring.pyx

@@ -56,7 +56,7 @@ import sage.rings.rational_field
 import sage.rings.ideal
 import sage.libs.pari.all
 import sage.rings.ideal
-from sage.categories.basic import EuclideanDomains
+from sage.categories.basic import EuclideanDomains, DedekindDomains
 from sage.categories.infinite_enumerated_sets import InfiniteEnumeratedSets
 from sage.rings.number_field.number_field_element_base import NumberFieldElement_base
 from sage.structure.coerce cimport is_numpy_type
@@ -122,7 +122,8 @@ cdef class IntegerRing_class(PrincipalIdealDomain):
         sage: Z.is_field()
         False
         sage: Z.category()
-        Join of Category of euclidean domains
+        Join of Category of Dedekind domains
+            and Category of euclidean domains
             and Category of infinite enumerated sets
             and Category of metric spaces
         sage: Z(2^(2^5) + 1)
@@ -312,7 +313,7 @@ cdef class IntegerRing_class(PrincipalIdealDomain):
             True
         """
         Parent.__init__(self, base=self, names=('x',), normalize=False,
-                        category=(EuclideanDomains(), InfiniteEnumeratedSets().Metric()))
+                        category=(EuclideanDomains(), DedekindDomains(), InfiniteEnumeratedSets().Metric()))
         self._populate_coercion_lists_(init_no_parent=True,
                                        convert_method_name='_integer_')
 
@@ -852,17 +853,6 @@ cdef class IntegerRing_class(PrincipalIdealDomain):
         except TypeError:
             return False
 
-    def is_noetherian(self):
-        """
-        Return ``True`` since the integers are a Noetherian ring.
-
-        EXAMPLES::
-
-            sage: ZZ.is_noetherian()
-            True
-        """
-        return True
-
     def _repr_option(self, key):
         """
         Metadata about the :meth:`_repr_` output.
@@ -1132,6 +1122,11 @@ cdef class IntegerRing_class(PrincipalIdealDomain):
         """
         Return the Krull dimension of the integers, which is 1.
 
+        .. NOTE::
+
+            This should rather be inherited from the category
+            of ``DedekindDomains``.
+
         EXAMPLES::
 
             sage: ZZ.krull_dimension()
@@ -1143,6 +1138,11 @@ cdef class IntegerRing_class(PrincipalIdealDomain):
         """
         Return that the integer ring is, in fact, integrally closed.
 
+        .. NOTE::
+
+            This should rather be inherited from the category
+            of ``DedekindDomains``.
+
         EXAMPLES::
 
             sage: ZZ.is_integrally_closed()

src/sage/rings/ring.pyx

@@ -1753,137 +1753,6 @@ cdef class NoetherianRing(CommutativeRing):
         """
         return True
 
-cdef class DedekindDomain(IntegralDomain):
-    """
-    Generic Dedekind domain class.
-
-    A Dedekind domain is a Noetherian integral domain of Krull
-    dimension one that is integrally closed in its field of fractions.
-
-    This class is deprecated, and not actually used anywhere in the
-    Sage code base.  If you think you need it, please create a
-    category :class:`DedekindDomains`, move the code of this class
-    there, and use it instead.
-    """
-    def krull_dimension(self):
-        """
-        Return 1 since Dedekind domains have Krull dimension 1.
-
-        EXAMPLES:
-
-        The following are examples of Dedekind domains (Noetherian integral
-        domains of Krull dimension one that are integrally closed over its
-        field of fractions)::
-
-            sage: ZZ.krull_dimension()
-            1
-            sage: x = polygen(ZZ, 'x')
-            sage: K = NumberField(x^2 + 1, 's')                                         # needs sage.rings.number_field
-            sage: OK = K.ring_of_integers()                                             # needs sage.rings.number_field
-            sage: OK.krull_dimension()                                                  # needs sage.rings.number_field
-            1
-
-        The following are not Dedekind domains but have
-        a ``krull_dimension`` function::
-
-            sage: QQ.krull_dimension()
-            0
-            sage: T.<x,y> = PolynomialRing(QQ,2); T
-            Multivariate Polynomial Ring in x, y over Rational Field
-            sage: T.krull_dimension()
-            2
-            sage: U.<x,y,z> = PolynomialRing(ZZ,3); U
-            Multivariate Polynomial Ring in x, y, z over Integer Ring
-            sage: U.krull_dimension()
-            4
-
-            sage: # needs sage.rings.number_field
-            sage: K.<i> = QuadraticField(-1)
-            sage: R = K.order(2*i); R
-            Order of conductor 2 generated by 2*i
-             in Number Field in i with defining polynomial x^2 + 1 with i = 1*I
-            sage: R.is_maximal()
-            False
-            sage: R.krull_dimension()
-            1
-        """
-        return 1
-
-    def is_integrally_closed(self):
-        """
-        Return ``True`` since Dedekind domains are integrally closed.
-
-        EXAMPLES:
-
-        The following are examples of Dedekind domains (Noetherian integral
-        domains of Krull dimension one that are integrally closed over its
-        field of fractions).
-
-        ::
-
-            sage: ZZ.is_integrally_closed()
-            True
-            sage: x = polygen(ZZ, 'x')
-            sage: K = NumberField(x^2 + 1, 's')                                         # needs sage.rings.number_field
-            sage: OK = K.ring_of_integers()                                             # needs sage.rings.number_field
-            sage: OK.is_integrally_closed()                                             # needs sage.rings.number_field
-            True
-
-        These, however, are not Dedekind domains::
-
-            sage: QQ.is_integrally_closed()
-            True
-            sage: S = ZZ[sqrt(5)]; S.is_integrally_closed()                             # needs sage.rings.number_field sage.symbolic
-            False
-            sage: T.<x,y> = PolynomialRing(QQ, 2); T
-            Multivariate Polynomial Ring in x, y over Rational Field
-            sage: T.is_integral_domain()
-            True
-        """
-        return True
-
-    def integral_closure(self):
-        r"""
-        Return ``self`` since Dedekind domains are integrally closed.
-
-        EXAMPLES::
-
-            sage: # needs sage.rings.number_field
-            sage: x = polygen(ZZ, 'x')
-            sage: K = NumberField(x^2 + 1, 's')
-            sage: OK = K.ring_of_integers()
-            sage: OK.integral_closure()
-            Gaussian Integers generated by s in Number Field in s
-             with defining polynomial x^2 + 1
-            sage: OK.integral_closure() == OK
-            True
-
-            sage: QQ.integral_closure() == QQ
-            True
-        """
-        return self
-
-    def is_noetherian(self):
-        r"""
-        Return ``True`` since Dedekind domains are Noetherian.
-
-        EXAMPLES:
-
-        The integers, `\ZZ`, and rings of integers of number
-        fields are Dedekind domains::
-
-            sage: ZZ.is_noetherian()
-            True
-            sage: x = polygen(ZZ, 'x')
-            sage: K = NumberField(x^2 + 1, 's')                                         # needs sage.rings.number_field
-            sage: OK = K.ring_of_integers()                                             # needs sage.rings.number_field
-            sage: OK.is_noetherian()                                                    # needs sage.rings.number_field
-            True
-            sage: QQ.is_noetherian()
-            True
-        """
-        return True
-
 
 cdef class PrincipalIdealDomain(IntegralDomain):
     """