sage.rings.abc: Add IntegerModRing, Order; use them in sage.matrix, s…

…age.modules

src/sage/matrix/matrix0.pyx

@@ -44,7 +44,7 @@ from sage.categories.integral_domains import IntegralDomains
 
 from sage.rings.ring cimport CommutativeRing
 from sage.rings.ring import is_Ring
-from sage.rings.finite_rings.integer_mod_ring import is_IntegerModRing
+import sage.rings.abc
 from sage.rings.integer_ring import is_IntegerRing
 
 import sage.modules.free_module
@@ -5749,7 +5749,7 @@ cdef class Matrix(sage.structure.element.Matrix):
         R = self.base_ring()
         if algorithm is None and R in _Fields:
             return ~self
-        elif algorithm is None and is_IntegerModRing(R):
+        elif algorithm is None and isinstance(R, sage.rings.abc.IntegerModRing):
             # Finite fields are handled above.
             # This is "easy" in that we either get an error or
             # the right answer. Note that of course there

src/sage/modules/free_module.py

@@ -172,7 +172,7 @@
 import sage.rings.ring as ring
 import sage.rings.integer_ring
 import sage.rings.rational_field
-import sage.rings.finite_rings.integer_mod_ring
+import sage.rings.abc
 import sage.rings.infinity
 import sage.rings.integer
 from sage.categories.principal_ideal_domains import PrincipalIdealDomains
@@ -253,7 +253,7 @@ def create_object(self, version, key):
             elif base_ring in PrincipalIdealDomains():
                 return FreeModule_ambient_pid(base_ring, rank, sparse=sparse)
 
-            elif isinstance(base_ring, sage.rings.number_field.order.Order) \
+            elif isinstance(base_ring, sage.rings.abc.Order) \
                 and base_ring.is_maximal() and base_ring.class_number() == 1:
                 return FreeModule_ambient_pid(base_ring, rank, sparse=sparse)
 
@@ -7434,7 +7434,7 @@ def element_class(R, is_sparse):
     elif sage.rings.rational_field.is_RationalField(R) and not is_sparse:
         from .vector_rational_dense import Vector_rational_dense
         return Vector_rational_dense
-    elif sage.rings.finite_rings.integer_mod_ring.is_IntegerModRing(R) and not is_sparse:
+    elif isinstance(R, sage.rings.abc.IntegerModRing) and not is_sparse:
         from .vector_mod2_dense import Vector_mod2_dense
         if R.order() == 2:
             return Vector_mod2_dense

src/sage/rings/abc.pyx

@@ -32,3 +32,18 @@ cdef class ComplexDoubleField(Field):
     """
 
     pass
+
+
+class IntegerModRing:
+    r"""
+    Abstract base class for :class:`~sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic`.
+    """
+
+    pass
+
+class Order:
+    r"""
+    Abstract base class for :class:`~sage.rings.number_field.order.Order`.
+    """
+
+    pass

src/sage/rings/finite_rings/integer_mod_ring.py

@@ -297,7 +297,7 @@ def _unit_gens_primepowercase(p, r):
 
 
 @richcmp_method
-class IntegerModRing_generic(quotient_ring.QuotientRing_generic):
+class IntegerModRing_generic(quotient_ring.QuotientRing_generic, IntegerModRing):
     """
     The ring of integers modulo `N`.
 

src/sage/rings/number_field/order.py

@@ -47,6 +47,7 @@
 from sage.rings.ring import IntegralDomain
 from sage.structure.sequence import Sequence
 from sage.rings.integer_ring import ZZ
+import sage.rings.abc
 from sage.structure.element import is_Element
 from .number_field_element import OrderElement_absolute, OrderElement_relative
 
@@ -126,7 +127,7 @@ def EquationOrder(f, names, **kwds):
     return K.order(K.gens())
 
 
-class Order(IntegralDomain):
+class Order(IntegralDomain, sage.rings.abc.Order):
     r"""
     An order in a number field.