Merge #32665

src/sage/calculus/all.py

@@ -58,8 +58,8 @@ def symbolic_expression(x):
         2*x^2 + 3
         sage: type(a)
         <class 'sage.symbolic.expression.Expression'>
-        sage: from sage.symbolic.expression import is_Expression
-        sage: is_Expression(a)
+        sage: from sage.structure.element import Expression
+        sage: isinstance(a, Expression)
         True
         sage: a in SR
         True

src/sage/calculus/integration.pyx

@@ -605,8 +605,8 @@ def monte_carlo_integral(func, xl, xu, size_t calls, algorithm='plain',
                               "more items in upper and lower limits"
                              ).format(len(vars), tuple(vars), target_dim))
 
-        from sage.symbolic.expression import is_Expression
-        if is_Expression(func):
+        from sage.structure.element import Expression
+        if isinstance(func, Expression):
             if params:
                 to_sub = dict(zip(vars[-len(params):], params))
                 func = func.subs(to_sub)

src/sage/dynamics/arithmetic_dynamics/affine_ds.py

@@ -56,9 +56,9 @@ class initialization directly.
 from sage.schemes.affine.affine_subscheme import AlgebraicScheme_subscheme_affine
 from sage.schemes.generic.morphism import SchemeMorphism_polynomial
 from sage.structure.element import get_coercion_model
-from sage.symbolic.ring import is_SymbolicExpressionRing
-from sage.symbolic.ring import var
-from sage.symbolic.ring import SR
+
+import sage.rings.abc
+
 
 class DynamicalSystem_affine(SchemeMorphism_polynomial_affine_space,
                              DynamicalSystem):
@@ -275,7 +275,7 @@ def __classcall_private__(cls, morphism_or_polys, domain=None):
             else:
                 polys = [PR(poly) for poly in polys]
         if domain is None:
-            if PR is SR:
+            if isinstance(PR, sage.rings.abc.SymbolicRing):
                 raise TypeError("Symbolic Ring cannot be the base ring")
             if fraction_field:
                 PR = PR.ring()
@@ -292,7 +292,7 @@ def __classcall_private__(cls, morphism_or_polys, domain=None):
         if len(polys) != domain.ambient_space().coordinate_ring().ngens():
             raise ValueError('Number of polys does not match dimension of {}'.format(domain))
         R = domain.base_ring()
-        if R is SR:
+        if isinstance(R, sage.rings.abc.SymbolicRing):
             raise TypeError("Symbolic Ring cannot be the base ring")
         if not is_AffineSpace(domain) and not isinstance(domain, AlgebraicScheme_subscheme_affine):
             raise ValueError('"domain" must be an affine scheme')
@@ -529,7 +529,8 @@ def dynatomic_polynomial(self, period):
         F = G.dynatomic_polynomial(period)
         T = G.domain().coordinate_ring()
         S = self.domain().coordinate_ring()
-        if is_SymbolicExpressionRing(F.parent()):
+        if isinstance(F.parent(), sage.rings.abc.SymbolicRing):
+            from sage.symbolic.ring import var
             u = var(self.domain().coordinate_ring().variable_name())
             return F.subs({F.variables()[0]:u,F.variables()[1]:1})
         elif T(F.denominator()).degree() == 0:

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/ext/fast_callable.pyx

@@ -308,6 +308,7 @@ from sage.rings.all import RDF, CDF
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
 from sage.structure.element cimport parent
+from sage.structure.element cimport Expression as Expression_abc
 
 
 def fast_callable(x, domain=None, vars=None,
@@ -427,20 +428,16 @@ def fast_callable(x, domain=None, vars=None,
         et = x
         vars = et._etb._vars
     else:
-        from sage.symbolic.callable import is_CallableSymbolicExpression
-        from sage.symbolic.expression import is_Expression
-
         if not vars:
             # fast_float passes empty list/tuple
             vars = None
 
-        if is_CallableSymbolicExpression(x):
+        if isinstance(x, Expression_abc) and x.is_callable():
             if vars is None:
                 vars = x.arguments()
             if expect_one_var and len(vars) != 1:
                 raise ValueError(f"passed expect_one_var=True, but the callable expression takes {len(vars)} arguments")
-        elif is_Expression(x):
-            from sage.symbolic.ring import is_SymbolicVariable
+        elif isinstance(x, Expression_abc):
             if vars is None:
                 vars = x.variables()
                 if expect_one_var and len(vars) <= 1:
@@ -449,7 +446,7 @@ def fast_callable(x, domain=None, vars=None,
                 else:
                     raise ValueError("list of variables must be specified for symbolic expressions")
             def to_var(var):
-                if is_SymbolicVariable(var):
+                if isinstance(var, Expression_abc) and var.is_symbol():
                     return var
                 from sage.symbolic.ring import SR
                 return SR.var(var)
@@ -999,8 +996,7 @@ cdef class Expression:
             return ExpressionIPow(es._etb, s, o)
         else:
             # I really don't like this, but I can't think of a better way
-            from sage.symbolic.expression import is_Expression
-            if is_Expression(o) and o in ZZ:
+            if isinstance(o, Expression_abc) and o in ZZ:
                 es = s
                 return ExpressionIPow(es._etb, s, ZZ(o))
             else:

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.integer_ring 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/interfaces/qepcad.py

@@ -1924,11 +1924,9 @@ def atomic(self, lhs, op='=', rhs=0):
         if isinstance(lhs, qformula):
             return lhs
 
-        from sage.symbolic.expression import is_SymbolicEquation
-        if is_SymbolicEquation(lhs):
-            rhs = lhs.rhs()
-            op = lhs.operator()
-            lhs = lhs.lhs()
+        from sage.structure.element import Expression
+        if isinstance(lhs, Expression) and lhs.is_relational():
+            lhs, op, rhs = lhs.lhs(), lhs.operator(), lhs.rhs()
 
         op = self._normalize_op(op)
 

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

@@ -94,6 +94,7 @@ from sage.rings.complex_double import CDF
 from sage.rings.real_mpfr import RealField
 from sage.rings.complex_mpfr import ComplexField
 from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
+import sage.rings.abc
 from sage.arith.numerical_approx cimport digits_to_bits
 from copy import copy
 
@@ -821,8 +822,7 @@ 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()
@@ -1984,9 +1984,6 @@ 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
         n = self._ncols
 
@@ -2030,7 +2027,7 @@ 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.
@@ -2075,7 +2072,7 @@ cdef class Matrix(Matrix1):
         # is then assumed to not be a variable in the symbolic ring.  But this
         # resulted in further exceptions/ errors.
 
-        var = 'A0123456789' if is_SymbolicExpressionRing(R) else 'x'
+        var = 'A0123456789' if isinstance(R, sage.rings.abc.SymbolicRing) else 'x'
         try:
             charp = self.charpoly(var, algorithm="df")
         except ValueError:
@@ -14722,6 +14719,8 @@ 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/misc/sageinspect.py

@@ -2317,7 +2317,7 @@ def sage_getsourcelines(obj):
         ...)
         sage: x = var('x')
         sage: lines, lineno = sage_getsourcelines(x); lines[0:5]
-        ['cdef class Expression(CommutativeRingElement):\n',
+        ['cdef class Expression(...):\n',
          '\n',
          '    cdef GEx _gobj\n',
          '\n',