sage.structure, sage.rings, sage.matrix: Use sage.rings.abc for Integ…

…erModRing

src/sage/matrix/matrix2.pyx

@@ -95,6 +95,7 @@ from sage.rings.real_mpfr import RealField
 from sage.rings.complex_mpfr import ComplexField
 from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
 from sage.misc.derivative import multi_derivative
+import sage.rings.abc
 from sage.arith.numerical_approx cimport digits_to_bits
 from copy import copy
 
@@ -822,8 +823,7 @@ cdef class Matrix(Matrix1):
         if not K.is_integral_domain():
             # The non-integral-domain case is handled almost entirely
             # separately.
-            from sage.rings.finite_rings.integer_mod_ring import is_IntegerModRing
-            if is_IntegerModRing(K):
+            if isinstance(K, sage.rings.abc.IntegerModRing):
                 from sage.libs.pari import pari
                 A = pari(self.lift())
                 b = pari(B).lift()
@@ -1985,7 +1985,6 @@ cdef class Matrix(Matrix1):
             sage: A.determinant() == B.determinant()
             True
         """
-        from sage.rings.finite_rings.integer_mod_ring import is_IntegerModRing
         from sage.symbolic.ring import is_SymbolicExpressionRing
 
         cdef Py_ssize_t n
@@ -2031,7 +2030,7 @@ cdef class Matrix(Matrix1):
             return d
 
         # Special case for Z/nZ or GF(p):
-        if is_IntegerModRing(R) and self.is_dense():
+        if isinstance(R, sage.rings.abc.IntegerModRing) and self.is_dense():
             import sys
             # If the characteristic is prime and smaller than a machine
             # word, use PARI.
@@ -14723,6 +14722,8 @@ cdef class Matrix(Matrix1):
             for i from 0 <= i < size:
                 PyList_Append(M,<object>f(<object>PyList_GET_ITEM(L,i)))
 
+            from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
+
             return MatrixSpace(IntegerModRing(2),
                                nrows=self._nrows,ncols=self._ncols).matrix(M)
 

src/sage/matrix/matrix_space.py

@@ -236,7 +236,7 @@ def get_matrix_class(R, nrows, ncols, sparse, implementation):
                     except ImportError:
                         pass
 
-            if sage.rings.finite_rings.integer_mod_ring.is_IntegerModRing(R):
+            if isinstance(R, sage.rings.abc.IntegerModRing):
                 from . import matrix_modn_dense_double, matrix_modn_dense_float
                 if R.order() < matrix_modn_dense_float.MAX_MODULUS:
                     return matrix_modn_dense_float.Matrix_modn_dense_float
@@ -326,7 +326,7 @@ def get_matrix_class(R, nrows, ncols, sparse, implementation):
     if implementation is not None:
         raise ValueError("cannot choose an implementation for sparse matrices")
 
-    if sage.rings.finite_rings.integer_mod_ring.is_IntegerModRing(R) and R.order() < matrix_modn_sparse.MAX_MODULUS:
+    if isinstance(R, sage.rings.abc.IntegerModRing) and R.order() < matrix_modn_sparse.MAX_MODULUS:
         return matrix_modn_sparse.Matrix_modn_sparse
 
     if sage.rings.rational_field.is_RationalField(R):

src/sage/rings/finite_rings/finite_field_base.pyx

@@ -40,6 +40,7 @@ from sage.misc.persist import register_unpickle_override
 from sage.misc.cachefunc import cached_method
 from sage.misc.prandom import randrange
 from sage.rings.integer cimport Integer
+import sage.rings.abc
 from sage.misc.superseded import deprecation_cython as deprecation
 
 # Copied from sage.misc.fast_methods, used in __hash__() below.
@@ -1342,10 +1343,9 @@ cdef class FiniteField(Field):
             False
         """
         from sage.rings.integer_ring import ZZ
-        from sage.rings.finite_rings.integer_mod_ring import is_IntegerModRing
         if R is int or R is long or R is ZZ:
             return True
-        if is_IntegerModRing(R) and self.characteristic().divides(R.characteristic()):
+        if isinstance(R, sage.rings.abc.IntegerModRing) and self.characteristic().divides(R.characteristic()):
             return R.hom((self.one(),), check=False)
         if is_FiniteField(R):
             if R is self:

src/sage/structure/parent.pyx

@@ -2642,8 +2642,8 @@ cdef class Parent(sage.structure.category_object.CategoryObject):
         elif self_on_left and op is operator.pow:
             S_is_int = parent_is_integers(S)
             if not S_is_int:
-                from sage.rings.finite_rings.integer_mod_ring import is_IntegerModRing
-                if is_IntegerModRing(S):
+                from sage.rings.abc import IntegerModRing
+                if isinstance(S, IntegerModRing):
                     # We allow powering by an IntegerMod by treating it
                     # as an integer.
                     #