git grep -l -E 'is_(Real|Complex)(Double)?Field' | xargs sed -E -i.ba…

…k 's/^from sage[.]rings.*import is_((Real|Complex)(Double)?Field) *$/import sage.rings.abc/;s/is_((Real|Complex)(Double)?Field)[(]([^)]*)[)]/isinstance(\4, sage.rings.abc.\1)/g;'

src/sage/dynamics/arithmetic_dynamics/projective_ds.py

@@ -2065,7 +2065,7 @@ def canonical_height(self, P, **kwds):
         # 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.
         for v in emb:
-            if is_RealField(v.codomain()) or v.codomain() is RDF:
+            if isinstance(v.codomain(, sage.rings.abc.RealField)) or v.codomain() is RDF:
                 dv = R.one()
             else:
                 dv = R(2)

src/sage/functions/orthogonal_polys.py

@@ -304,8 +304,8 @@
 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
+import sage.rings.abc
 
 from sage.symbolic.function import BuiltinFunction, GinacFunction
 from sage.symbolic.expression import Expression
@@ -672,7 +672,7 @@ 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) and not isinstance(real_parent, 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 +681,7 @@ 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) and not isinstance(real_parent, 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 +1031,7 @@ 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) and not isinstance(real_parent, 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 +1040,7 @@ 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) and not isinstance(real_parent, 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

@@ -365,7 +365,7 @@ def elliptic_j(z, prec=53):
 
     CC = z.parent()
     from sage.rings.complex_mpfr import is_ComplexField
-    if not is_ComplexField(CC):
+    if not isinstance(CC, sage.rings.abc.ComplexField):
         CC = ComplexField(prec)
         try:
             z = CC(z)

src/sage/matrix/misc.pyx

@@ -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(, sage.rings.abc.RealField)):
         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

@@ -7443,9 +7443,9 @@ 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 sage.rings.real_double.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 sage.rings.complex_double.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

@@ -338,7 +338,7 @@ def __init__(self, X, P, codomain=None, check=False):
         """
         if codomain is None:
             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

@@ -15,7 +15,7 @@
 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  ------------------
@@ -278,7 +278,7 @@ 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:
         R = RealField()

src/sage/rings/complex_double.pyx

@@ -111,16 +111,16 @@ from sage.structure.richcmp cimport rich_to_bool
 cimport gmpy2
 gmpy2.import_gmpy2()
 
-def is_ComplexDoubleField(x):
+def isinstance(x, sage.rings.abc.ComplexDoubleField):
     """
     Return ``True`` if ``x`` is the complex double field.
 
     EXAMPLES::
 
         sage: from sage.rings.complex_double import is_ComplexDoubleField
-        sage: is_ComplexDoubleField(CDF)
+        sage: isinstance(CDF, sage.rings.abc.ComplexDoubleField)
         True
-        sage: is_ComplexDoubleField(ComplexField(53))
+        sage: isinstance(ComplexField(53, sage.rings.abc.ComplexDoubleField))
         False
     """
     return isinstance(x, ComplexDoubleField_class)

src/sage/rings/complex_mpfr.pyx

@@ -157,7 +157,7 @@ def is_ComplexNumber(x):
     """
     return isinstance(x, ComplexNumber)
 
-def is_ComplexField(x):
+def isinstance(x, sage.rings.abc.ComplexField):
     """
     Check if ``x`` is a :class:`complex field <ComplexField_class>`.
 
@@ -543,7 +543,7 @@ class ComplexField_class(ring.Field):
         RR = self._real_field()
         if RR.has_coerce_map_from(S):
             return RRtoCC(RR, self) * RR._internal_coerce_map_from(S)
-        if is_ComplexField(S):
+        if isinstance(S, sage.rings.abc.ComplexField):
             if self._prec <= S._prec:
                 return self._generic_coerce_map(S)
             else:

src/sage/rings/number_field/number_field.py

@@ -9949,12 +9949,12 @@ def hilbert_symbol(self, a, b, P = None):
             from sage.rings.complex_interval_field import is_ComplexIntervalField
             from sage.rings.real_mpfr import is_RealField
             from sage.rings.all import (AA, CDF, QQbar, RDF)
-            if is_ComplexField(codom) or is_ComplexIntervalField(codom) or \
+            if isinstance(codom, sage.rings.abc.ComplexField) or is_ComplexIntervalField(codom) or \
                                          codom is CDF or codom is QQbar:
                 if P(self.gen()).imag() == 0:
                     raise ValueError("Possibly real place (=%s) given as complex embedding in hilbert_symbol. Is it real or complex?" % P)
                 return 1
-            if is_RealField(codom) or codom is RDF or codom is AA:
+            if isinstance(codom, sage.rings.abc.RealField) or codom is RDF or codom is AA:
                 if P(a) > 0 or P(b) > 0:
                     return 1
                 return -1
@@ -12317,7 +12317,7 @@ def refine_embedding(e, prec=None):
         return e
 
     # We first compute all the embeddings at the new precision:
-    if sage.rings.real_mpfr.is_RealField(RC) or RC in (RDF, RLF):
+    if sage.rings.real_mpfr.isinstance(RC, sage.rings.abc.RealField) or RC in (RDF, RLF):
         if prec == Infinity:
             elist = K.embeddings(sage.rings.qqbar.AA)
         else:

src/sage/rings/number_field/number_field_element.pyx

@@ -3946,7 +3946,7 @@ cdef class NumberFieldElement(FieldElement):
             return Kv.zero()
         ht = a.log()
         from sage.rings.real_mpfr import is_RealField
-        if weighted and not is_RealField(Kv):
+        if weighted and not isinstance(Kv, sage.rings.abc.RealField):
             ht*=2
         return ht
 

src/sage/rings/polynomial/multi_polynomial_libsingular.pyx

@@ -224,8 +224,8 @@ from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
 from sage.rings.finite_rings.finite_field_prime_modn import FiniteField_prime_modn
 from sage.rings.rational cimport Rational
 from sage.rings.rational_field import QQ
-from sage.rings.complex_mpfr import is_ComplexField
-from sage.rings.real_mpfr import is_RealField
+import sage.rings.abc
+import sage.rings.abc
 from sage.rings.integer_ring import is_IntegerRing, ZZ
 from sage.rings.integer cimport Integer
 from sage.rings.integer import GCD_list
@@ -1366,14 +1366,14 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_base):
 
         base_ring = self.base_ring()
 
-        if is_RealField(base_ring):
+        if isinstance(base_ring, sage.rings.abc.RealField):
             # singular converts to bits from base_10 in mpr_complex.cc by:
             #  size_t bits = 1 + (size_t) ((float)digits * 3.5);
             precision = base_ring.precision()
             digits = ceil((2*precision - 2)/7.0)
             self.__singular = singular.ring("(real,%d,0)"%digits, _vars, order=order)
 
-        elif is_ComplexField(base_ring):
+        elif isinstance(base_ring, sage.rings.abc.ComplexField):
             # singular converts to bits from base_10 in mpr_complex.cc by:
             #  size_t bits = 1 + (size_t) ((float)digits * 3.5);
             precision = base_ring.precision()

src/sage/rings/polynomial/polynomial_element.pyx

@@ -7912,25 +7912,25 @@ cdef class Polynomial(CommutativeAlgebraElement):
 
         late_import()
 
-        input_fp = (is_RealField(K)
-                    or is_ComplexField(K)
-                    or is_RealDoubleField(K)
-                    or is_ComplexDoubleField(K))
-        output_fp = (is_RealField(L)
-                     or is_ComplexField(L)
-                     or is_RealDoubleField(L)
-                     or is_ComplexDoubleField(L))
-        input_complex = (is_ComplexField(K)
-                         or is_ComplexDoubleField(K))
-        output_complex = (is_ComplexField(L)
-                          or is_ComplexDoubleField(L))
+        input_fp = (isinstance(K, sage.rings.abc.RealField)
+                    or isinstance(K, sage.rings.abc.ComplexField)
+                    or isinstance(K, sage.rings.abc.RealDoubleField)
+                    or isinstance(K, sage.rings.abc.ComplexDoubleField))
+        output_fp = (isinstance(L, sage.rings.abc.RealField)
+                     or isinstance(L, sage.rings.abc.ComplexField)
+                     or isinstance(L, sage.rings.abc.RealDoubleField)
+                     or isinstance(L, sage.rings.abc.ComplexDoubleField))
+        input_complex = (isinstance(K, sage.rings.abc.ComplexField)
+                         or isinstance(K, sage.rings.abc.ComplexDoubleField))
+        output_complex = (isinstance(L, sage.rings.abc.ComplexField)
+                          or isinstance(L, sage.rings.abc.ComplexDoubleField))
         input_gaussian = (isinstance(K, NumberField_quadratic)
                           and list(K.polynomial()) == [1, 0, 1])
 
         if input_fp and output_fp:
             # allow for possibly using a fast but less reliable
             # floating point algorithm from numpy
-            low_prec = is_RealDoubleField(K) or is_ComplexDoubleField(K)
+            low_prec = isinstance(K, sage.rings.abc.RealDoubleField) or isinstance(K, sage.rings.abc.ComplexDoubleField)
             if algorithm is None:
                 if low_prec:
                     algorithm = 'either'
@@ -7943,8 +7943,8 @@ cdef class Polynomial(CommutativeAlgebraElement):
             # We should support GSL, too.  We could also support PARI's
             # old Newton-iteration algorithm.
 
-            input_arbprec = (is_RealField(K) or
-                             is_ComplexField(K))
+            input_arbprec = (isinstance(K, sage.rings.abc.RealField) or
+                             isinstance(K, sage.rings.abc.ComplexField))
 
             if algorithm == 'numpy' or algorithm == 'either':
                 if K.prec() > 53 and L.prec() > 53:
@@ -8082,7 +8082,7 @@ cdef class Polynomial(CommutativeAlgebraElement):
                 # If we want the complex roots, and the input is not
                 # floating point, we convert to a real polynomial
                 # (except when the input coefficients are Gaussian rationals).
-                if is_ComplexDoubleField(L):
+                if isinstance(L, sage.rings.abc.ComplexDoubleField):
                     real_field = RDF
                 else:
                     real_field = RealField(L.prec())
@@ -8250,7 +8250,7 @@ cdef class Polynomial(CommutativeAlgebraElement):
             True
         """
         K = self.base_ring()
-        if is_RealField(K) or is_RealDoubleField(K):
+        if isinstance(K, sage.rings.abc.RealField) or isinstance(K, sage.rings.abc.RealDoubleField):
             return self.roots(multiplicities=False)
 
         return self.roots(ring=RR, multiplicities=False)
@@ -8292,11 +8292,11 @@ cdef class Polynomial(CommutativeAlgebraElement):
             True
         """
         K = self.base_ring()
-        if is_RealField(K):
+        if isinstance(K, sage.rings.abc.RealField):
             return self.roots(ring=ComplexField(K.prec()), multiplicities=False)
-        if is_RealDoubleField(K):
+        if isinstance(K, sage.rings.abc.RealDoubleField):
             return self.roots(ring=CDF, multiplicities=False)
-        if is_ComplexField(K) or is_ComplexDoubleField(K):
+        if isinstance(K, sage.rings.abc.ComplexField) or isinstance(K, sage.rings.abc.ComplexDoubleField):
             return self.roots(multiplicities=False)
 
         return self.roots(ring=CC, multiplicities=False)

src/sage/rings/polynomial/polynomial_ring.py

@@ -165,7 +165,7 @@
 from sage.misc.cachefunc import cached_method
 from sage.misc.lazy_attribute import lazy_attribute
 
-from sage.rings.real_mpfr import is_RealField
+import sage.rings.abc
 from sage.rings.fraction_field_element import FractionFieldElement
 from sage.rings.finite_rings.element_base import FiniteRingElement
 
@@ -1995,7 +1995,7 @@ def __init__(self, base_ring, name="x", sparse=False, element_class=None, catego
                 else:
                     from sage.rings.polynomial.polynomial_number_field import Polynomial_relative_number_field_dense
                     element_class = Polynomial_relative_number_field_dense
-            elif is_RealField(base_ring):
+            elif isinstance(base_ring, sage.rings.abc.RealField):
                 element_class = PolynomialRealDense
             elif isinstance(base_ring, sage.rings.complex_arb.ComplexBallField):
                 from sage.rings.polynomial.polynomial_complex_arb import Polynomial_complex_arb