formal deprecation for Dedekind domains (sigh)

src/sage/categories/fields.py

@@ -118,9 +118,9 @@ def __contains__(self, x):
             0
 
         """
-        import sage.rings.ring
+        from sage.rings.ring import _is_Field
         try:
-            return self._contains_helper(x) or sage.rings.ring._is_Field(x)
+            return self._contains_helper(x) or _is_Field(x)
         except Exception:
             return False
 

src/sage/modular/pollack_stevens/distributions.py

@@ -49,7 +49,7 @@
 from sage.categories.modules import Modules
 from sage.structure.factory import UniqueFactory
 
-import sage.rings.ring as ring
+from sage.rings.ring import Ring
 
 lazy_import('sage.modular.pollack_stevens.dist', 'get_dist_classes')
 lazy_import('sage.rings.padics.factory', ['ZpCA', 'QpCR'])
@@ -281,7 +281,7 @@ def __init__(self, k, p=None, prec_cap=None, base=None, character=None,
             ...
             ValueError: p must be prime
         """
-        if not isinstance(base, ring.Ring):
+        if not isinstance(base, Ring):
             raise TypeError("base must be a ring")
         #from sage.rings.padics.pow_computer import PowComputer
         # should eventually be the PowComputer on ZpCA once that uses longs.

src/sage/modules/free_module.py

@@ -186,7 +186,7 @@
 import sage.rings.integer
 import sage.rings.integer_ring
 import sage.rings.rational_field
-import sage.rings.ring as ring
+from sage.rings.ring import IntegralDomain, is_Ring
 from sage.categories.infinite_enumerated_sets import InfiniteEnumeratedSets
 from sage.categories.integral_domains import IntegralDomains
 from sage.categories.principal_ideal_domains import PrincipalIdealDomains
@@ -213,6 +213,7 @@
 )
 from sage.structure.sequence import Sequence
 
+
 ###############################################################################
 #
 # Constructor functions
@@ -294,7 +295,7 @@ def create_object(self, version, key):
             and base_ring.is_maximal() and base_ring.class_number() == 1):
             return FreeModule_ambient_pid(base_ring, rank, sparse=sparse)
 
-        if isinstance(base_ring, ring.IntegralDomain) or base_ring in IntegralDomains():
+        if isinstance(base_ring, IntegralDomain) or base_ring in IntegralDomains():
             return FreeModule_ambient_domain(base_ring, rank, sparse=sparse)
 
         return FreeModule_ambient(base_ring, rank, sparse=sparse)
@@ -725,7 +726,7 @@ def span(gens, base_ring=None, check=True, already_echelonized=False):
         TypeError: generators must be lists of ring elements
         or free module elements!
     """
-    if ring.is_Ring(gens):
+    if is_Ring(gens):
         # we allow the old input format with first input the base_ring.
         # Do we want to deprecate it?..
         base_ring, gens = gens, base_ring

src/sage/modules/free_quadratic_module.py

@@ -69,7 +69,7 @@
 
 import sage.matrix.matrix_space
 import sage.misc.latex as latex
-import sage.rings.ring as ring
+from sage.rings.ring import Field, IntegralDomain
 from sage.categories.principal_ideal_domains import PrincipalIdealDomains
 from sage.modules import free_module
 
@@ -174,7 +174,7 @@ def FreeQuadraticModule(base_ring, rank, inner_product_matrix,
         M = FreeQuadraticModule_ambient_pid(
             base_ring, rank, sparse=sparse, inner_product_matrix=inner_product_matrix)
 
-    elif isinstance(base_ring, ring.IntegralDomain) or base_ring.is_integral_domain():
+    elif isinstance(base_ring, IntegralDomain) or base_ring.is_integral_domain():
         M = FreeQuadraticModule_ambient_domain(
             base_ring, rank, sparse=sparse, inner_product_matrix=inner_product_matrix)
     else:
@@ -713,7 +713,7 @@ def __init__(self, base_field, dimension, degree, inner_product_matrix, sparse=F
             [0 0 0 0 0 1 0]
             [0 0 0 0 0 0 1]
         """
-        if not isinstance(base_field, ring.Field):
+        if not isinstance(base_field, Field):
             raise TypeError("the base_field (=%s) must be a field" % base_field)
         free_module.FreeModule_generic_field.__init__(
             self, base_field=base_field, dimension=dimension, degree=degree, sparse=sparse)

src/sage/rings/all.py

@@ -16,7 +16,9 @@
 
 # Ring base classes
 from sage.rings.ring import (Ring, Field, CommutativeRing, IntegralDomain,
-                             DedekindDomain, PrincipalIdealDomain)
+                             PrincipalIdealDomain)
+
+lazy_import("sage.rings.ring", "DedekindDomain")
 
 # Ring element base classes
 from sage.structure.element import (CommutativeAlgebraElement,

src/sage/rings/complex_double.pxd

@@ -1,7 +1,6 @@
 from sage.libs.gsl.types cimport gsl_complex
 
 cimport sage.structure.element
-cimport sage.rings.ring
 cimport sage.rings.abc
 
 

src/sage/rings/complex_double.pyx

@@ -79,7 +79,6 @@ cdef extern from "<complex.h>":
     double cabs(double complex)
 
 import sage.rings.abc
-cimport sage.rings.ring
 cimport sage.rings.integer
 
 from sage.structure.element cimport Element, FieldElement

src/sage/rings/complex_mpc.pxd

@@ -1,7 +1,7 @@
 from sage.libs.mpc.types cimport mpc_t, mpc_rnd_t
 
 cimport sage.structure.element
-cimport sage.rings.ring
+from sage.rings.ring cimport Field
 
 cdef class MPComplexNumber(sage.structure.element.FieldElement):
     cdef mpc_t value
@@ -10,7 +10,7 @@ cdef class MPComplexNumber(sage.structure.element.FieldElement):
     cpdef _add_(self, other) noexcept
     cpdef _mul_(self, other) noexcept
 
-cdef class MPComplexField_class(sage.rings.ring.Field):
+cdef class MPComplexField_class(Field):
     cdef readonly int _prec
     cdef mpc_rnd_t __rnd
     cdef object __rnd_str

src/sage/rings/complex_mpc.pyx

@@ -257,7 +257,7 @@ def MPComplexField(prec=53, rnd="RNDNN", names=None):
     return C
 
 
-cdef class MPComplexField_class(sage.rings.ring.Field):
+cdef class MPComplexField_class(Field):
     def __init__(self, int prec=53, rnd="RNDNN"):
         """
         Initialize ``self``.

src/sage/rings/finite_rings/integer_mod_ring.py

@@ -65,7 +65,7 @@
 from sage.arith.misc import factor
 from sage.arith.misc import primitive_root
 from sage.arith.misc import CRT_basis
-import sage.rings.ring as ring
+from sage.rings.ring import Field, CommutativeRing
 import sage.rings.abc
 from sage.rings.finite_rings import integer_mod
 import sage.rings.integer as integer
@@ -85,6 +85,7 @@ class PariError(Exception):
 
 from sage.interfaces.abc import GapElement
 
+
 class IntegerModFactory(UniqueFactory):
     r"""
     Return the quotient ring `\ZZ / n\ZZ`.
@@ -1261,7 +1262,7 @@ def _coerce_map_from_(self, S):
         elif S is integer_ring.ZZ:
             return integer_mod.Integer_to_IntegerMod(self)
         elif isinstance(S, IntegerModRing_generic):
-            if isinstance(S, ring.Field):
+            if isinstance(S, Field):
                 return None
             try:
                 return integer_mod.IntegerMod_to_IntegerMod(S, self)
@@ -1554,7 +1555,7 @@ def random_element(self, bound=None):
             True
         """
         if bound is not None:
-            return ring.CommutativeRing.random_element(self, bound)
+            return CommutativeRing.random_element(self, bound)
         a = random.randint(0, self.order() - 1)
         return self(a)
 

src/sage/rings/number_field/number_field.py

@@ -100,7 +100,7 @@
 from sage.rings.finite_rings.integer_mod import mod
 from sage.categories.number_fields import NumberFields
 
-import sage.rings.ring
+from sage.rings.ring import Ring
 from sage.misc.latex import latex_variable_name
 
 from .unit_group import UnitGroup
@@ -3536,7 +3536,7 @@ def ideal(self, *gens, **kwds):
         try:
             return self.fractional_ideal(*gens, **kwds)
         except ValueError:
-            return sage.rings.ring.Ring.ideal(self, gens, **kwds)
+            return Ring.ideal(self, gens, **kwds)
 
     def idealchinese(self, ideals, residues):
         r"""

src/sage/rings/pari_ring.py

@@ -17,7 +17,7 @@
 #                  http://www.gnu.org/licenses/
 # ****************************************************************************
 import sage.libs.pari.all as pari
-import sage.rings.ring as ring
+from sage.rings.ring import Ring
 from sage.structure.element import RingElement
 from sage.structure.richcmp import richcmp
 from sage.misc.fast_methods import Singleton
@@ -158,7 +158,7 @@ def __int__(self):
         return int(self.__x)
 
 
-class PariRing(Singleton, ring.Ring):
+class PariRing(Singleton, Ring):
     """
     EXAMPLES::
 
@@ -170,7 +170,7 @@ class PariRing(Singleton, ring.Ring):
     Element = Pari
 
     def __init__(self):
-        ring.Ring.__init__(self, self)
+        Ring.__init__(self, self)
 
     def __repr__(self):
         return 'Pseudoring of all PARI objects.'

src/sage/rings/polynomial/multi_polynomial_ring_base.pxd

@@ -1,7 +1,7 @@
-cimport sage.rings.ring
+from sage.rings.ring cimport CommutativeRing, Ring
 from sage.structure.parent cimport Parent
 
-cdef class MPolynomialRing_base(sage.rings.ring.CommutativeRing):
+cdef class MPolynomialRing_base(CommutativeRing):
     cdef object _ngens
     cdef object _term_order
     cdef public object _has_singular

src/sage/rings/polynomial/multi_polynomial_ring_base.pyx

@@ -32,7 +32,7 @@ def is_MPolynomialRing(x):
     return isinstance(x, MPolynomialRing_base)
 
 
-cdef class MPolynomialRing_base(sage.rings.ring.CommutativeRing):
+cdef class MPolynomialRing_base(CommutativeRing):
     def __init__(self, base_ring, n, names, order):
         """
         Create a polynomial ring in several variables over a commutative ring.
@@ -93,7 +93,7 @@ cdef class MPolynomialRing_base(sage.rings.ring.CommutativeRing):
             category = categories.rings.Rings().Finite()
         else:
             category = polynomial_default_category(base_ring.category(), n)
-        sage.rings.ring.Ring.__init__(self, base_ring, names, category=category)
+        Ring.__init__(self, base_ring, names, category=category)
 
     def is_integral_domain(self, proof=True):
         """

src/sage/rings/polynomial/polynomial_ring.py

@@ -148,7 +148,8 @@
 import sage.categories as categories
 from sage.categories.morphism import IdentityMorphism
 
-import sage.rings.ring as ring
+from sage.rings.ring import (Algebra, CommutativeAlgebra, IntegralDomain,
+                             PrincipalIdealDomain, is_Ring)
 from sage.structure.element import is_RingElement
 import sage.rings.rational_field as rational_field
 from sage.rings.rational_field import QQ
@@ -225,7 +226,7 @@ def is_PolynomialRing(x):
 
 #########################################################################################
 
-class PolynomialRing_general(ring.Algebra):
+class PolynomialRing_general(Algebra):
     """
     Univariate polynomial ring over a ring.
     """
@@ -302,7 +303,7 @@ def __init__(self, base_ring, name=None, sparse=False, implementation=None,
         self.Element = self._polynomial_class
         self.__cyclopoly_cache = {}
         self._has_singular = False
-        ring.Algebra.__init__(self, base_ring, names=name, normalize=True, category=category)
+        Algebra.__init__(self, base_ring, names=name, normalize=True, category=category)
         self._populate_coercion_lists_(convert_method_name='_polynomial_')
 
     def __reduce__(self):
@@ -1708,7 +1709,7 @@ def monics( self, of_degree=None, max_degree=None ):
         raise ValueError("you should pass exactly one of of_degree and max_degree")
 
 
-class PolynomialRing_commutative(PolynomialRing_general, ring.CommutativeAlgebra):
+class PolynomialRing_commutative(PolynomialRing_general, CommutativeAlgebra):
     """
     Univariate polynomial ring over a commutative ring.
     """
@@ -1835,7 +1836,7 @@ def _roots_univariate_polynomial(self, p, ring=None, multiplicities=True, algori
 
 
 class PolynomialRing_integral_domain(PolynomialRing_commutative, PolynomialRing_singular_repr,
-                                     ring.IntegralDomain):
+                                     IntegralDomain):
     def __init__(self, base_ring, name="x", sparse=False, implementation=None,
             element_class=None, category=None):
         """
@@ -2055,8 +2056,9 @@ def construction(self):
         return categories.pushout.PolynomialFunctor(self.variable_name(), sparse=self.is_sparse(),
                                                     implementation=implementation), self.base_ring()
 
+
 class PolynomialRing_field(PolynomialRing_integral_domain,
-                           ring.PrincipalIdealDomain):
+                           PrincipalIdealDomain):
     def __init__(self, base_ring, name="x", sparse=False, implementation=None,
                  element_class=None, category=None):
         """
@@ -3594,7 +3596,7 @@ def polygen(ring_or_element, name="x"):
     """
     if is_RingElement(ring_or_element):
         base_ring = ring_or_element.parent()
-    elif ring.is_Ring(ring_or_element):
+    elif is_Ring(ring_or_element):
         base_ring = ring_or_element
     else:
         raise TypeError("input must be a ring or ring element")

src/sage/rings/polynomial/polynomial_ring_constructor.py

@@ -21,7 +21,7 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 from sage.structure.category_object import normalize_names
-import sage.rings.ring as ring
+from sage.rings.ring import is_Ring, IntegralDomain
 
 try:
     import sage.rings.padics.padic_base_leaves as padic_base_leaves
@@ -621,7 +621,7 @@ def PolynomialRing(base_ring, *args, **kwds):
         sage: R.<x,y> = PolynomialRing(RIF,2)
         sage: TestSuite(R).run(skip=['_test_elements', '_test_elements_eq_transitive'])
     """
-    if not ring.is_Ring(base_ring):
+    if not is_Ring(base_ring):
         raise TypeError("base_ring {!r} must be a ring".format(base_ring))
 
     n = -1  # Unknown number of variables
@@ -860,7 +860,7 @@ def _multi_variate(base_ring, names, sparse=None, order="degrevlex", implementat
 
     if R is None and implementation == "generic":
         from . import multi_polynomial_ring
-        if isinstance(base_ring, ring.IntegralDomain):
+        if isinstance(base_ring, IntegralDomain):
             constructor = multi_polynomial_ring.MPolynomialRing_polydict_domain
         else:
             constructor = multi_polynomial_ring.MPolynomialRing_polydict

src/sage/rings/qqbar.py

@@ -560,7 +560,6 @@
 
 import sage.rings.abc
 import sage.rings.number_field.number_field_base
-import sage.rings.ring
 from sage.arith.misc import factor
 from sage.categories.action import Action
 from sage.misc.cachefunc import cached_method

src/sage/rings/real_mpfr.pxd

@@ -1,6 +1,5 @@
 from sage.libs.mpfr.types cimport mpfr_rnd_t, mpfr_t, mpfr_prec_t
 
-cimport sage.rings.ring
 cimport sage.rings.abc
 cimport sage.structure.element