Deprecate is_AlgebraicNumber, is_AlgebraicReal, is_ComplexDoubleElement, is_ComplexIntervalFieldElement, is_ComplexNumber, is_FractionField, is_FractionFieldElement, is_Integer, is_IntegerMod, is_IntegerRing, is_Rational, is_RationalField, is_RealDoubleElement, is_RealIntervalField, is_RealIntervalFieldElement, is_RealNumber

src/sage/algebras/quatalg/quaternion_algebra.py

@@ -51,7 +51,7 @@
 from sage.rings.rational import Rational
 from sage.rings.finite_rings.finite_field_constructor import GF
 from sage.rings.ideal import Ideal_fractional
-from sage.rings.rational_field import is_RationalField, QQ
+from sage.rings.rational_field import RationalField, QQ
 from sage.rings.infinity import infinity
 from sage.rings.number_field.number_field_base import NumberField
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
@@ -429,7 +429,7 @@ def is_division_algebra(self) -> bool:
             ...
             NotImplementedError: base field must be rational numbers
         """
-        if not is_RationalField(self.base_ring()):
+        if not isinstance(self.base_ring(), RationalField):
             raise NotImplementedError("base field must be rational numbers")
         return self.discriminant() != 1
 
@@ -453,7 +453,7 @@ def is_matrix_ring(self) -> bool:
             NotImplementedError: base field must be rational numbers
 
         """
-        if not is_RationalField(self.base_ring()):
+        if not isinstance(self.base_ring(), RationalField):
             raise NotImplementedError("base field must be rational numbers")
         return self.discriminant() == 1
 
@@ -678,7 +678,7 @@ def __init__(self, base_ring, a, b, names='i,j,k'):
         Parent.__init__(self, base=base_ring, names=names, category=cat)
         self._a = a
         self._b = b
-        if is_RationalField(base_ring) and a.denominator() == 1 == b.denominator():
+        if isinstance(base_ring, RationalField) and a.denominator() == 1 == b.denominator():
             self.Element = QuaternionAlgebraElement_rational_field
         elif (isinstance(base_ring, NumberField) and base_ring.degree() > 2 and base_ring.is_absolute() and
               a.denominator() == 1 == b.denominator() and base_ring.defining_polynomial().is_monic()):
@@ -1066,7 +1066,7 @@ def is_definite(self):
             ...
             ValueError: base field must be rational numbers
         """
-        if not is_RationalField(self.base_ring()):
+        if not isinstance(self.base_ring(), RationalField):
             raise ValueError("base field must be rational numbers")
         a, b = self.invariants()
         return a < 0 and b < 0
@@ -1218,7 +1218,7 @@ def discriminant(self):
             sage: QuaternionAlgebra(QQ[sqrt(2)], 3, 19).discriminant()                  # needs sage.symbolic
             Fractional ideal (1)
         """
-        if not is_RationalField(self.base_ring()):
+        if not isinstance(self.base_ring(), RationalField):
             try:
                 F = self.base_ring()
                 return F.hilbert_conductor(self._a, self._b)
@@ -1245,7 +1245,7 @@ def ramified_primes(self):
             sage: QuaternionAlgebra(QQ, -58, -69).ramified_primes()
             [3, 23, 29]
         """
-        if not is_RationalField(self.base_ring()):
+        if not isinstance(self.base_ring(), RationalField):
             raise ValueError("base field must be the rational numbers")
 
         a, b = self._a, self._b
@@ -2517,7 +2517,7 @@ def attempt_isomorphism(self, other):
         if other.quaternion_algebra() != Q:
             raise TypeError('not an order in the same quaternion algebra')
 
-        if not is_RationalField(Q.base_ring()):
+        if not isinstance(Q.base_ring(), RationalField):
             raise NotImplementedError('only implemented for orders in a rational quaternion algebra')
         if not Q.is_definite():
             raise NotImplementedError('only implemented for definite quaternion orders')

src/sage/combinat/finite_state_machine_generators.py

@@ -268,8 +268,8 @@ def Word(self, word, input_alphabet=None):
 
         TESTS::
 
-            sage: from sage.rings.integer import is_Integer
-            sage: all(is_Integer(s.label()) for s in A.states())
+            sage: from sage.rings.integer import Integer
+            sage: all(isinstance(s.label(), Integer) for s in A.states())
             True
         """
         letters = list(word)

src/sage/combinat/sf/jack.py

@@ -36,7 +36,7 @@
 from sage.rings.rational_field import QQ
 from sage.arith.misc import gcd
 from sage.arith.functions import lcm
-from sage.rings.fraction_field import is_FractionField
+from sage.rings.fraction_field import FractionField_generic
 from sage.misc.misc_c import prod
 from sage.categories.morphism import SetMorphism
 from sage.categories.homset import Hom, End
@@ -481,7 +481,7 @@ def normalize_coefficients(self, c):
         6/(t^2 + 3*t + 2)
     """
     BR = self.base_ring()
-    if is_FractionField(BR) and BR.base_ring() == QQ:
+    if isinstance(BR, FractionField_generic) and BR.base_ring() == QQ:
         denom = c.denominator()
         numer = c.numerator()
 

src/sage/dynamics/arithmetic_dynamics/affine_ds.py

@@ -45,7 +45,7 @@ class initialization directly.
 from sage.rings.integer import Integer
 from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.fraction_field import FractionField
-from sage.rings.fraction_field import is_FractionField
+from sage.rings.fraction_field import FractionField_generic
 from sage.rings.quotient_ring import is_QuotientRing
 from sage.schemes.affine.affine_morphism import SchemeMorphism_polynomial_affine_space
 from sage.schemes.affine.affine_morphism import SchemeMorphism_polynomial_affine_space_field
@@ -261,7 +261,7 @@ def __classcall_private__(cls, morphism_or_polys, domain=None):
             polys = [morphism_or_polys]
 
         PR = get_coercion_model().common_parent(*polys)
-        fraction_field = any(is_FractionField(poly.parent()) for poly in polys)
+        fraction_field = any(isinstance(poly.parent(), FractionField_generic) for poly in polys)
         if fraction_field:
             K = PR.base_ring().fraction_field()
             # Replace base ring with its fraction field

src/sage/dynamics/arithmetic_dynamics/projective_ds.py

@@ -87,8 +87,8 @@ class initialization directly.
 from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.finite_rings.finite_field_constructor import GF
 from sage.rings.finite_rings.integer_mod_ring import Zmod
-from sage.rings.fraction_field import (FractionField, is_FractionField, FractionField_1poly_field)
-from sage.rings.fraction_field_element import is_FractionFieldElement, FractionFieldElement
+from sage.rings.fraction_field import FractionField, FractionField_generic, FractionField_1poly_field
+from sage.rings.fraction_field_element import FractionFieldElement
 from sage.rings.function_field.function_field import is_FunctionField
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
@@ -394,11 +394,11 @@ def __classcall_private__(cls, morphism_or_polys, domain=None, names=None):
             # homogenize!
             f = morphism_or_polys
             aff_CR = f.parent()
-            if (not is_PolynomialRing(aff_CR) and not is_FractionField(aff_CR)
+            if (not is_PolynomialRing(aff_CR) and not isinstance(aff_CR, FractionField_generic)
                 and not (is_MPolynomialRing(aff_CR) and aff_CR.ngens() == 1)):
                 msg = '{} is not a single variable polynomial or rational function'
                 raise ValueError(msg.format(f))
-            if is_FractionField(aff_CR):
+            if isinstance(aff_CR, FractionField_generic):
                 polys = [f.numerator(),f.denominator()]
             else:
                 polys = [f, aff_CR(1)]
@@ -889,7 +889,7 @@ def dynatomic_polynomial(self, period):
                         # do it again to divide out by denominators of coefficients
                         PHI = QR2[0].sage()
                         PHI = PHI.numerator()._maxima_().divide(PHI.denominator())[0].sage()
-                    if not is_FractionFieldElement(PHI):
+                    if not isinstance(PHI, FractionFieldElement):
                         from sage.symbolic.expression_conversions import polynomial
                         PHI = polynomial(PHI, ring=self.coordinate_ring())
                 except (TypeError, NotImplementedError): #something Maxima, or the conversion, can't handle
@@ -3533,7 +3533,7 @@ def affine_preperiodic_model(self, m, n, return_conjugation=False):
                         if hyperplane_found:
                             break
                 else:
-                    if is_PolynomialRing(R) or is_MPolynomialRing(R) or is_FractionField(R):
+                    if is_PolynomialRing(R) or is_MPolynomialRing(R) or isinstance(R, FractionField_generic):
                         # for polynomial rings, we can get an infinite family of hyperplanes
                         # by increasing the degree
                         var = R.gen()
@@ -3702,7 +3702,7 @@ def automorphism_group(self, **kwds):
             raise NotImplementedError("rational function of degree 1 not implemented")
         f = self.dehomogenize(1)
         R = PolynomialRing(f.base_ring(),'x')
-        if is_FractionFieldElement(f[0]):
+        if isinstance(f[0], FractionFieldElement):
             F = (f[0].numerator().univariate_polynomial(R))/f[0].denominator().univariate_polynomial(R)
         else:
             F = f[0].univariate_polynomial(R)
@@ -4880,7 +4880,7 @@ def periodic_points(self, n, minimal=True, formal=False, R=None, algorithm='vari
         if isinstance(R, FractionField_1poly_field) or is_FunctionField(R):
             raise NotImplementedError('periodic points not implemented for fraction function fields; '
                 'clear denominators and use the polynomial ring instead')
-        if is_FractionField(R):
+        if isinstance(R, FractionField_generic):
             if is_MPolynomialRing(R.ring()):
                 raise NotImplementedError('periodic points not implemented for fraction function fields; '
                     'clear denominators and use the polynomial ring instead')
@@ -5784,7 +5784,7 @@ def sigma_invariants(self, n, formal=False, embedding=None, type='point',
                     X = X.change_ring(F)
                 else:
                     F = base_ring
-                    if is_FractionField(base_ring):
+                    if isinstance(base_ring, FractionField_generic):
                         if is_MPolynomialRing(base_ring.ring()) or is_PolynomialRing(base_ring.ring()):
                             f.normalize_coordinates()
                             f_ring = f.change_ring(base_ring.ring())
@@ -5886,7 +5886,7 @@ def sigma_invariants(self, n, formal=False, embedding=None, type='point',
             return sigmas
 
         base_ring = dom.base_ring()
-        if is_FractionField(base_ring):
+        if isinstance(base_ring, FractionField_generic):
             base_ring = base_ring.ring()
         if (is_PolynomialRing(base_ring) or is_MPolynomialRing(base_ring)):
             base_ring = base_ring.base_ring()

src/sage/dynamics/complex_dynamics/mandel_julia.py

@@ -51,7 +51,7 @@
 from sage.schemes.projective.projective_space import ProjectiveSpace
 from sage.misc.prandom import randint
 from sage.calculus.var import var
-from sage.rings.fraction_field import is_FractionField
+from sage.rings.fraction_field import FractionField_generic
 from sage.categories.function_fields import FunctionFields
 
 lazy_import('sage.dynamics.arithmetic_dynamics.generic_ds', 'DynamicalSystem')
@@ -243,14 +243,14 @@ def mandelbrot_plot(f=None, **kwds):
         P = f.parent()
 
         if P.base_ring() is CC or P.base_ring() is CDF:
-            if is_FractionField(P):
+            if isinstance(P, FractionField_generic):
                 raise NotImplementedError("coefficients must be polynomials in the parameter")
             gen_list = list(P.gens())
             parameter = gen_list.pop(gen_list.index(parameter))
             variable = gen_list.pop()
 
         elif P.base_ring().base_ring() is CC or P.base_ring().base_ring() is CDF:
-            if is_FractionField(P.base_ring()):
+            if isinstance(P.base_ring(), FractionField_generic):
                 raise NotImplementedError("coefficients must be polynomials in the parameter")
             phi = P.flattening_morphism()
             f = phi(f)

src/sage/dynamics/complex_dynamics/mandel_julia_helper.pyx

@@ -34,7 +34,7 @@ from sage.ext.fast_callable import fast_callable
 from sage.calculus.all import symbolic_expression
 from sage.symbolic.ring import SR
 from sage.calculus.var import var
-from sage.rings.fraction_field import is_FractionField
+from sage.rings.fraction_field import FractionField_generic
 from sage.categories.function_fields import FunctionFields
 from cypari2.handle_error import PariError
 from math import sqrt
@@ -709,14 +709,14 @@ cpdef polynomial_mandelbrot(f, parameter=None, double x_center=0,
     P = f.parent()
 
     if P.base_ring() is CC:
-        if is_FractionField(P):
+        if isinstance(P, FractionField_generic):
             raise NotImplementedError("coefficients must be polynomials in the parameter")
         gen_list = list(P.gens())
         parameter = gen_list.pop(gen_list.index(parameter))
         variable = gen_list.pop()
 
     elif P.base_ring().base_ring() is CC:
-        if is_FractionField(P.base_ring()):
+        if isinstance(P.base_ring(), FractionField_generic):
             raise NotImplementedError("coefficients must be polynomials in the parameter")
         phi = P.flattening_morphism()
         f = phi(f)

src/sage/functions/transcendental.py

@@ -28,10 +28,10 @@
 
 lazy_import('sage.combinat.combinat', 'bernoulli_polynomial')
 lazy_import('sage.rings.cc', 'CC')
-lazy_import('sage.rings.complex_mpfr', ['ComplexField', 'is_ComplexNumber'])
+lazy_import('sage.rings.complex_mpfr', ['ComplexField', 'ComplexNumber'])
 lazy_import('sage.rings.polynomial.polynomial_real_mpfr_dense', 'PolynomialRealDense')
 lazy_import('sage.rings.real_double', 'RDF')
-lazy_import('sage.rings.real_mpfr', ['RR', 'RealField', 'is_RealNumber'])
+lazy_import('sage.rings.real_mpfr', ['RR', 'RealField', 'RealNumber'])
 
 lazy_import('sage.libs.mpmath.utils', 'call', as_='_mpmath_utils_call')
 lazy_import('mpmath', 'zeta', as_='_mpmath_zeta')
@@ -452,7 +452,7 @@ def zeta_symmetric(s):
     - I copied the definition of xi from
       http://web.viu.ca/pughg/RiemannZeta/RiemannZetaLong.html
     """
-    if not (is_ComplexNumber(s) or is_RealNumber(s)):
+    if not (isinstance(s, ComplexNumber) or isinstance(s, RealNumber)):
         s = ComplexField()(s)
 
     R = s.parent()
@@ -544,7 +544,7 @@ def _eval_(self, x):
             sage: dickman_rho(0)                                                        # needs sage.symbolic
             1.00000000000000
         """
-        if not is_RealNumber(x):
+        if not isinstance(x, RealNumber):
             try:
                 x = RR(x)
             except (TypeError, ValueError):

src/sage/groups/affine_gps/affine_group.py

@@ -173,8 +173,8 @@ def __classcall__(cls, *args, **kwds):
             ring = V.base_ring()
         if len(args) == 2:
             degree, ring = args
-            from sage.rings.integer import is_Integer
-            if is_Integer(ring):
+            from sage.rings.integer import Integer
+            if isinstance(ring, Integer):
                 from sage.rings.finite_rings.finite_field_constructor import FiniteField
                 var = kwds.get('var', 'a')
                 ring = FiniteField(ring, var)

src/sage/groups/matrix_gps/matrix_group.py

@@ -59,7 +59,7 @@
 
 from sage.categories.groups import Groups
 from sage.categories.rings import Rings
-from sage.rings.integer import is_Integer
+from sage.rings.integer import Integer
 from sage.matrix.matrix_space import MatrixSpace
 from sage.misc.latex import latex
 from sage.structure.richcmp import (richcmp_not_equal, rich_to_bool,
@@ -417,7 +417,7 @@ def __init__(self, degree, base_ring, category=None):
             True
         """
         assert base_ring in Rings
-        assert is_Integer(degree)
+        assert isinstance(degree, Integer)
 
         self._deg = degree
         if self._deg <= 0:

src/sage/matrix/matrix0.pyx

@@ -42,7 +42,7 @@ from sage.categories.commutative_rings import CommutativeRings
 from sage.categories.rings import Rings
 
 import sage.rings.abc
-from sage.rings.integer_ring import is_IntegerRing
+from sage.rings.integer_ring import IntegerRing_class
 
 import sage.modules.free_module
 
@@ -5975,7 +5975,7 @@ cdef class Matrix(sage.structure.element.Matrix):
                 return (~self.lift_centered()).change_ring(R)
             except (TypeError, ZeroDivisionError):
                 raise ZeroDivisionError("input matrix must be nonsingular")
-        elif algorithm is None and is_IntegerRing(R):
+        elif algorithm is None and isinstance(R, IntegerRing_class):
             try:
                 return (~self).change_ring(R)
             except (TypeError, ZeroDivisionError):

src/sage/matrix/matrix2.pyx

@@ -93,8 +93,8 @@ from sage.structure.element import Vector
 from sage.structure.element cimport have_same_parent
 from sage.misc.verbose import verbose
 from sage.rings.number_field.number_field_base import NumberField
-from sage.rings.integer_ring import ZZ, is_IntegerRing
-from sage.rings.rational_field import QQ, is_RationalField
+from sage.rings.integer_ring import ZZ, IntegerRing_class
+from sage.rings.rational_field import QQ, RationalField
 import sage.rings.abc
 from sage.arith.numerical_approx cimport digits_to_bits
 
@@ -4538,11 +4538,11 @@ cdef class Matrix(Matrix1):
             algorithm = 'default'
         elif algorithm not in ['default', 'generic', 'flint', 'pari', 'padic', 'pluq']:
             raise ValueError("matrix kernel algorithm '%s' not recognized" % algorithm)
-        elif algorithm == 'padic' and not (is_IntegerRing(R) or is_RationalField(R)):
+        elif algorithm == 'padic' and not (isinstance(R, IntegerRing_class) or isinstance(R, RationalField)):
             raise ValueError("'padic' matrix kernel algorithm only available over the rationals and the integers, not over %s" % R)
-        elif algorithm == 'flint' and not (is_IntegerRing(R) or is_RationalField(R)):
+        elif algorithm == 'flint' and not (isinstance(R, IntegerRing_class) or isinstance(R, RationalField)):
             raise ValueError("'flint' matrix kernel algorithm only available over the rationals and the integers, not over %s" % R)
-        elif algorithm == 'pari' and not (is_IntegerRing(R) or (isinstance(R, NumberField) and not is_RationalField(R))):
+        elif algorithm == 'pari' and not (isinstance(R, IntegerRing_class) or (isinstance(R, NumberField) and not isinstance(R, RationalField))):
             raise ValueError("'pari' matrix kernel algorithm only available over non-trivial number fields and the integers, not over %s" % R)
         elif algorithm == 'generic' and R not in _Fields:
             raise ValueError("'generic' matrix kernel algorithm only available over a field, not over %s" % R)
@@ -4557,7 +4557,7 @@ cdef class Matrix(Matrix1):
             raise ValueError("matrix kernel basis format '%s' not recognized" % basis)
         elif basis == 'pivot' and R not in _Fields:
             raise ValueError('pivot basis only available over a field, not over %s' % R)
-        elif basis == 'LLL' and not is_IntegerRing(R):
+        elif basis == 'LLL' and not isinstance(R, IntegerRing_class):
             raise ValueError('LLL-reduced basis only available over the integers, not over %s' % R)
         if basis == 'default':
             basis = 'echelon' if R in _Fields else 'computed'
@@ -4566,7 +4566,7 @@ cdef class Matrix(Matrix1):
         proof = kwds.pop('proof', None)
         if proof not in [None, True, False]:
             raise ValueError("'proof' must be one of True, False or None, not %s" % proof)
-        if not (proof is None or is_IntegerRing(R)):
+        if not (proof is None or isinstance(R, IntegerRing_class)):
             raise ValueError("'proof' flag only valid for matrices over the integers")
 
         # We could sanitize/process remaining (un-popped) keywords here and

src/sage/matrix/matrix_rational_dense.pyx

@@ -110,7 +110,7 @@ from sage.matrix.args cimport SparseEntry, MatrixArgs_init
 from sage.matrix.matrix_integer_dense cimport Matrix_integer_dense, _lift_crt
 from sage.structure.element cimport Element, Vector
 from sage.rings.integer cimport Integer
-from sage.rings.integer_ring import ZZ, is_IntegerRing
+from sage.rings.integer_ring import ZZ, IntegerRing_class
 import sage.rings.abc
 from sage.rings.rational_field import QQ
 
@@ -1465,7 +1465,7 @@ cdef class Matrix_rational_dense(Matrix_dense):
             if self._is_immutable:
                 return self
             return self.__copy__()
-        if is_IntegerRing(R):
+        if isinstance(R, IntegerRing_class):
             A, d = self._clear_denom()
             if not d.is_one():
                 raise TypeError("matrix has denominators so can't change to ZZ")