Merge #32612

src/sage/dynamics/arithmetic_dynamics/projective_ds.py

@@ -80,16 +80,15 @@ class initialization directly.
 from sage.rings.polynomial.flatten import FlatteningMorphism, UnflatteningMorphism
 from sage.rings.morphism import RingHomomorphism_im_gens
 from sage.rings.number_field.number_field_ideal import NumberFieldFractionalIdeal
-from sage.rings.number_field.number_field import is_NumberField
 from sage.rings.padics.all import Qp
 from sage.rings.polynomial.multi_polynomial_ring_base import is_MPolynomialRing
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
 from sage.rings.qqbar import QQbar, number_field_elements_from_algebraics
 from sage.rings.quotient_ring import QuotientRing_generic
 from sage.rings.rational_field import QQ
-from sage.rings.real_double import RDF
-from sage.rings.real_mpfr import (RealField, is_RealField)
+import sage.rings.abc
+from sage.rings.real_mpfr import RealField
 from sage.schemes.generic.morphism import SchemeMorphism_polynomial
 from sage.schemes.projective.projective_subscheme import AlgebraicScheme_subscheme_projective
 from sage.schemes.projective.projective_morphism import (
@@ -2062,10 +2061,10 @@ def canonical_height(self, P, **kwds):
 
         # Archimedean local heights
         # :: WARNING: If places is fed the default Sage precision of 53 bits,
-        # it uses Real or Complex Double Field in place of RealField(prec) or ComplexField(prec)
-        # the function is_RealField does not identify RDF as real, so we test for that ourselves.
+        # it uses Real or Complex Double Field in place of RealField(prec) or ComplexField(prec).
+        # RDF is an instance of a separate class.
         for v in emb:
-            if is_RealField(v.codomain()) or v.codomain() is RDF:
+            if isinstance(v.codomain(), (sage.rings.abc.RealField, sage.rings.abc.RealDoubleField)):
                 dv = R.one()
             else:
                 dv = R(2)

src/sage/functions/orthogonal_polys.py

@@ -304,8 +304,7 @@
 from sage.misc.latex import latex
 from sage.rings.all import ZZ, QQ, RR, CC
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-from sage.rings.real_mpfr import is_RealField
-from sage.rings.complex_mpfr import is_ComplexField
+import sage.rings.abc
 
 from sage.symbolic.function import BuiltinFunction, GinacFunction
 from sage.symbolic.expression import Expression
@@ -672,7 +671,7 @@ def _evalf_(self, n, x, **kwds):
         except KeyError:
             real_parent = parent(x)
 
-            if not is_RealField(real_parent) and not is_ComplexField(real_parent):
+            if not isinstance(real_parent, (sage.rings.abc.RealField, sage.rings.abc.ComplexField)):
                 # parent is not a real or complex field: figure out a good parent
                 if x in RR:
                     x = RR(x)
@@ -681,7 +680,7 @@ def _evalf_(self, n, x, **kwds):
                     x = CC(x)
                     real_parent = CC
 
-        if not is_RealField(real_parent) and not is_ComplexField(real_parent):
+        if not isinstance(real_parent, (sage.rings.abc.RealField, sage.rings.abc.ComplexField)):
             raise TypeError("cannot evaluate chebyshev_T with parent {}".format(real_parent))
 
         from sage.libs.mpmath.all import call as mpcall
@@ -1031,7 +1030,7 @@ def _evalf_(self, n, x, **kwds):
         except KeyError:
             real_parent = parent(x)
 
-            if not is_RealField(real_parent) and not is_ComplexField(real_parent):
+            if not isinstance(real_parent, (sage.rings.abc.RealField, sage.rings.abc.ComplexField)):
                 # parent is not a real or complex field: figure out a good parent
                 if x in RR:
                     x = RR(x)
@@ -1040,7 +1039,7 @@ def _evalf_(self, n, x, **kwds):
                     x = CC(x)
                     real_parent = CC
 
-        if not is_RealField(real_parent) and not is_ComplexField(real_parent):
+        if not isinstance(real_parent, (sage.rings.abc.RealField, sage.rings.abc.ComplexField)):
             raise TypeError("cannot evaluate chebyshev_U with parent {}".format(real_parent))
 
         from sage.libs.mpmath.all import call as mpcall

src/sage/functions/special.py

@@ -158,8 +158,8 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
+import sage.rings.abc
 from sage.rings.integer import Integer
-from sage.rings.complex_mpfr import ComplexField
 from sage.misc.latex import latex
 from sage.rings.all import ZZ
 from sage.symbolic.constants import pi
@@ -362,10 +362,9 @@ def elliptic_j(z, prec=53):
         sage: (-elliptic_j(tau, 100).real().round())^(1/3)
         640320
     """
-
     CC = z.parent()
-    from sage.rings.complex_mpfr import is_ComplexField
-    if not is_ComplexField(CC):
+    if not isinstance(CC, sage.rings.abc.ComplexField):
+        from sage.rings.complex_mpfr import ComplexField
         CC = ComplexField(prec)
         try:
             z = CC(z)

src/sage/libs/singular/ring.pyx

@@ -31,7 +31,7 @@ from sage.libs.singular.decl cimport rDefault, GFInfo, ZnmInfo, nInitChar, AlgEx
 from sage.rings.integer cimport Integer
 from sage.rings.integer_ring cimport IntegerRing_class
 from sage.rings.integer_ring import ZZ
-from sage.rings.finite_rings.integer_mod_ring import is_IntegerModRing
+import sage.rings.abc
 from sage.rings.number_field.number_field_base cimport NumberField
 from sage.rings.rational_field import RationalField
 from sage.rings.finite_rings.finite_field_base import FiniteField as FiniteField_generic
@@ -324,7 +324,7 @@ cdef ring *singular_ring_new(base_ring, n, names, term_order) except NULL:
 
         _ring = rDefault (_cf ,nvars, _names, nblcks, _order, _block0, _block1, _wvhdl)
 
-    elif is_IntegerModRing(base_ring):
+    elif isinstance(base_ring, sage.rings.abc.IntegerModRing):
 
         ch = base_ring.characteristic()
         if ch < 2:

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/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_rational_dense.pyx

@@ -109,7 +109,7 @@ from sage.rings.integer cimport Integer
 from sage.rings.ring import is_Ring
 from sage.rings.integer_ring import ZZ, is_IntegerRing
 from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
-from sage.rings.finite_rings.integer_mod_ring import is_IntegerModRing
+import sage.rings.abc
 from sage.rings.rational_field import QQ
 from sage.arith.all import gcd
 
@@ -1487,7 +1487,7 @@ cdef class Matrix_rational_dense(Matrix_dense):
             return A
 
         from .matrix_modn_dense_double import MAX_MODULUS
-        if is_IntegerModRing(R) and R.order() < MAX_MODULUS:
+        if isinstance(R, sage.rings.abc.IntegerModRing) and R.order() < MAX_MODULUS:
             b = R.order()
             A, d = self._clear_denom()
             if not b.gcd(d).is_one():

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/matrix/misc.pyx

@@ -40,7 +40,7 @@ from sage.rings.rational_field import QQ
 from sage.rings.integer cimport Integer
 from sage.arith.all import previous_prime, CRT_basis
 
-from sage.rings.real_mpfr import  is_RealField
+from sage.rings.real_mpfr cimport RealField_class
 from sage.rings.real_mpfr cimport RealNumber
 
 
@@ -510,7 +510,7 @@ def hadamard_row_bound_mpfr(Matrix A):
         ...
         OverflowError: cannot convert float infinity to integer
     """
-    if not is_RealField(A.base_ring()):
+    if not isinstance(A.base_ring(), RealField_class):
         raise TypeError("A must have base field an mpfr real field.")
 
     cdef RealNumber a, b

src/sage/modular/dirichlet.py

@@ -68,7 +68,7 @@
 
 from sage.categories.map import Map
 from sage.rings.rational_field import is_RationalField
-from sage.rings.complex_mpfr import is_ComplexField
+import sage.rings.abc
 from sage.rings.qqbar import is_AlgebraicField
 from sage.rings.ring import is_Ring
 
@@ -1153,7 +1153,7 @@ def _pari_init_(self):
 
         # now compute the input for pari (list of exponents)
         P = self.parent()
-        if is_ComplexField(P.base_ring()):
+        if isinstance(P.base_ring(), sage.rings.abc.ComplexField):
             zeta = P.zeta()
             zeta_argument = zeta.argument()
             v = [int(x.argument() / zeta_argument) for x in values_on_gens]
@@ -1345,7 +1345,7 @@ def gauss_sum(self, a=1):
         K = G.base_ring()
         chi = self
         m = G.modulus()
-        if is_ComplexField(K):
+        if isinstance(K, sage.rings.abc.ComplexField):
             return self.gauss_sum_numerical(a=a)
         elif is_AlgebraicField(K):
             L = K
@@ -1422,7 +1422,7 @@ def gauss_sum_numerical(self, prec=53, a=1):
         """
         G = self.parent()
         K = G.base_ring()
-        if is_ComplexField(K):
+        if isinstance(K, sage.rings.abc.ComplexField):
 
             def phi(t):
                 return t
@@ -2138,7 +2138,7 @@ def element(self):
         """
         P = self.parent()
         M = P._module
-        if is_ComplexField(P.base_ring()):
+        if isinstance(P.base_ring(), sage.rings.abc.ComplexField):
             zeta = P.zeta()
             zeta_argument = zeta.argument()
             v = M([int(round(x.argument() / zeta_argument))
@@ -2607,7 +2607,7 @@ def _zeta_powers(self):
         w = [a]
         zeta = self.zeta()
         zeta_order = self.zeta_order()
-        if is_ComplexField(R):
+        if isinstance(R, sage.rings.abc.ComplexField):
             for i in range(1, zeta_order):
                 a = a * zeta
                 a._set_multiplicative_order(zeta_order / gcd(zeta_order, i))

src/sage/modules/free_module.py

@@ -170,9 +170,10 @@
 from sage.modules.module import Module
 import sage.rings.finite_rings.finite_field_constructor as finite_field
 import sage.rings.ring as ring
+import sage.rings.abc
 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 +254,7 @@ 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 +7435,7 @@ 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
@@ -7443,9 +7444,9 @@ def element_class(R, is_sparse):
             return Vector_modn_dense
         else:
             return free_module_element.FreeModuleElement_generic_dense
-    elif sage.rings.real_double.is_RealDoubleField(R) and not is_sparse:
+    elif isinstance(R, sage.rings.abc.RealDoubleField) and not is_sparse:
         return sage.modules.vector_real_double_dense.Vector_real_double_dense
-    elif sage.rings.complex_double.is_ComplexDoubleField(R) and not is_sparse:
+    elif isinstance(R, sage.rings.abc.ComplexDoubleField) and not is_sparse:
         return sage.modules.vector_complex_double_dense.Vector_complex_double_dense
     elif sage.symbolic.ring.is_SymbolicExpressionRing(R) and not is_sparse:
         import sage.modules.vector_symbolic_dense

src/sage/probability/random_variable.py

@@ -15,10 +15,10 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
+import sage.rings.abc
 from sage.structure.parent import Parent
 from sage.functions.log import log
 from sage.functions.all import sqrt
-from sage.rings.real_mpfr import (RealField, is_RealField)
 from sage.rings.rational_field import is_RationalField
 from sage.sets.set import Set
 from pprint import pformat
@@ -83,6 +83,7 @@ def __init__(self, X, f, codomain=None, check=False):
         if check:
             raise NotImplementedError("Not implemented")
         if codomain is None:
+            from sage.rings.real_mpfr import RealField
             RR = RealField()
         else:
             RR = codomain
@@ -337,8 +338,9 @@ def __init__(self, X, P, codomain=None, check=False):
             1.50000000000000
         """
         if codomain is None:
+            from sage.rings.real_mpfr import RealField
             codomain = RealField()
-        if not is_RealField(codomain) and not is_RationalField(codomain):
+        if not isinstance(codomain, sage.rings.abc.RealField) and not is_RationalField(codomain):
             raise TypeError("Argument codomain (= %s) must be the reals or rationals" % codomain)
         if check:
             one = sum(P.values())

src/sage/quadratic_forms/special_values.py

@@ -9,13 +9,12 @@
 
 from sage.combinat.combinat import bernoulli_polynomial
 from sage.misc.functional import denominator
-from sage.rings.all import RealField
 from sage.arith.all import kronecker_symbol, bernoulli, factorial, fundamental_discriminant
 from sage.rings.infinity import infinity
 from sage.rings.integer_ring import ZZ
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.rational_field import QQ
-from sage.rings.real_mpfr import is_RealField
+import sage.rings.abc
 from sage.symbolic.constants import pi, I
 
 # ---------------- The Gamma Function  ------------------
@@ -278,9 +277,10 @@ def quadratic_L_function__numerical(n, d, num_terms=1000):
         ....:         print("Oops! We have a problem at d = {}: exact = {}, numerical = {}".format(d, RR(quadratic_L_function__exact(1, d)), RR(quadratic_L_function__numerical(1, d))))
     """
     # Set the correct precision if it is given (for n).
-    if is_RealField(n.parent()):
+    if isinstance(n.parent(), sage.rings.abc.RealField):
         R = n.parent()
     else:
+        from sage.rings.real_mpfr import RealField
         R = RealField()
 
     if n < 0: