New ABC sage.structure.element.NumberFieldElement, deprecate is_NumberFieldElement

src/sage/interfaces/maxima_lib.py

@@ -1164,6 +1164,8 @@ def reduce_load_MaximaLib():
 import sage.rings.real_double
 import sage.symbolic.expression
 import sage.symbolic.integration.integral
+
+from sage.structure.element import NumberFieldElement
 from sage.symbolic.operators import FDerivativeOperator, add_vararg, mul_vararg
 
 car=EclObject("car")
@@ -1523,9 +1525,11 @@ def pyobject_to_max(obj):
     """
     if isinstance(obj,sage.rings.rational.Rational):
         return EclObject(obj) if (obj.denom().is_one()) else EclObject([[rat], obj.numer(),obj.denom()])
-    elif isinstance(obj,sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic) and obj.parent().defining_polynomial().list() == [1,0,1]:
-        re, im = obj.list()
-        return EclObject([[mplus], pyobject_to_max(re), [[mtimes], pyobject_to_max(im), max_i]])
+    elif isinstance(obj, NumberFieldElement):
+        from sage.rings.number_field.number_field_element_quadratic import NumberFieldElement_quadratic
+        if isinstance(obj, NumberFieldElement_quadratic) and obj.parent().defining_polynomial().list() == [1,0,1]:
+            re, im = obj.list()
+            return EclObject([[mplus], pyobject_to_max(re), [[mtimes], pyobject_to_max(im), max_i]])
     return EclObject(obj)
 
 # This goes from SR to EclObject

src/sage/rings/finite_rings/residue_field.pyx

@@ -160,9 +160,8 @@ from sage.rings.finite_rings.finite_field_ntl_gf2e import FiniteField_ntl_gf2e
 from sage.rings.finite_rings.finite_field_prime_modn import FiniteField_prime_modn
 from sage.rings.finite_rings.finite_field_pari_ffelt import FiniteField_pari_ffelt
 from sage.rings.ideal import is_Ideal
-from sage.structure.element cimport Element
+from sage.structure.element cimport Element, NumberFieldElement
 
-from sage.rings.number_field.number_field_element import is_NumberFieldElement
 from sage.rings.number_field.number_field_ideal import is_NumberFieldIdeal
 
 from sage.modules.free_module_element import FreeModuleElement
@@ -295,7 +294,7 @@ class ResidueFieldFactory(UniqueFactory):
             if not is_Ideal(p):
                 if isinstance(p, (int, Integer, Rational)):
                     p = ZZ.ideal(p)
-                elif is_NumberFieldElement(p):
+                elif isinstance(p, NumberFieldElement):
                     if p.parent().is_field():
                         p = p.parent().ring_of_integers().ideal(p)
                     else:

src/sage/rings/integer_ring.pyx

@@ -60,6 +60,7 @@ from sage.categories.basic import EuclideanDomains
 from sage.categories.infinite_enumerated_sets import InfiniteEnumeratedSets
 from sage.structure.coerce cimport is_numpy_type
 from sage.structure.element cimport parent
+from sage.structure.element import NumberFieldElement
 from sage.structure.parent_gens import ParentWithGens
 from sage.structure.parent cimport Parent
 from sage.structure.richcmp cimport rich_to_bool
@@ -414,7 +415,6 @@ cdef class IntegerRing_class(PrincipalIdealDomain):
         if x in self:
             return self
 
-        from sage.rings.number_field.number_field_element import NumberFieldElement
         if isinstance(x, NumberFieldElement):
             K, from_K = parent(x).subfield(x)
             return K.order(K.gen())

src/sage/rings/number_field/number_field_element.pxd

@@ -3,13 +3,15 @@ from sage.libs.gmp.types cimport mpz_t
 from sage.rings.integer cimport Integer
 from sage.rings.polynomial.polynomial_element cimport Polynomial
 from sage.structure.element cimport FieldElement, RingElement, ModuleElement
+from sage.structure.element cimport NumberFieldElement as NumberFieldElement_base
 from sage.structure.parent cimport Parent
 from sage.structure.parent_base cimport ParentWithBase
 from sage.libs.ntl.types cimport ZZ_c, ZZX_c
 from sage.libs.ntl.ntl_ZZX cimport ntl_ZZX
 from sage.libs.ntl.ntl_ZZ cimport ntl_ZZ
 
-cdef class NumberFieldElement(FieldElement):
+
+cdef class NumberFieldElement(NumberFieldElement_base):
     cdef ZZX_c __numerator
     cdef ZZ_c __denominator
     # Pointers to the defining polynomial (with numerator) for the field.

src/sage/rings/number_field/number_field_element.pyx

@@ -108,11 +108,19 @@ def is_NumberFieldElement(x):
 
         sage: from sage.rings.number_field.number_field_element import is_NumberFieldElement
         sage: is_NumberFieldElement(2)
+        doctest:warning...
+        DeprecationWarning: is_NumberFieldElement is deprecated;
+        use isinstance(..., sage.structure.element.NumberFieldElement) instead
+        See https://trac.sagemath.org/34931 for details.
         False
         sage: k.<a> = NumberField(x^7 + 17*x + 1)
         sage: is_NumberFieldElement(a+1)
         True
     """
+    from sage.misc.superseded import deprecation
+    deprecation(34931,
+                'is_NumberFieldElement is deprecated; '
+                'use isinstance(..., sage.structure.element.NumberFieldElement) instead')
     return isinstance(x, NumberFieldElement)
 
 
@@ -190,7 +198,7 @@ def _inverse_mod_generic(elt, I):
     return I.small_residue(y)
 
 
-cdef class NumberFieldElement(FieldElement):
+cdef class NumberFieldElement(NumberFieldElement_base):
     """
     An element of a number field.
 
@@ -3858,7 +3866,7 @@ cdef class NumberFieldElement(FieldElement):
         """
         from .number_field_ideal import is_NumberFieldIdeal
         if not is_NumberFieldIdeal(P):
-            if is_NumberFieldElement(P):
+            if isinstance(P, NumberFieldElement):
                 P = self.number_field().fractional_ideal(P)
             else:
                 raise TypeError("P must be an ideal")

src/sage/rings/universal_cyclotomic_field.py

@@ -167,7 +167,8 @@
 
 from sage.structure.richcmp import rich_to_bool
 from sage.structure.unique_representation import UniqueRepresentation
-from sage.structure.element import FieldElement, parent
+from sage.structure.element import FieldElement, parent, NumberFieldElement
+
 from sage.structure.coerce import py_scalar_to_element
 from sage.categories.morphism import Morphism
 from sage.rings.ring import Field
@@ -1537,7 +1538,6 @@ def _element_constructor_(self, elt):
         import sage.rings.abc
         P = parent(elt)
         if isinstance(P, sage.rings.abc.NumberField_cyclotomic):
-            from sage.rings.number_field.number_field_element import NumberFieldElement
             if isinstance(elt, NumberFieldElement):
                 from sage.rings.number_field.number_field import CyclotomicField
                 n = P.gen().multiplicative_order()

src/sage/schemes/elliptic_curves/cm.py

@@ -42,6 +42,8 @@
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 
 from sage.misc.cachefunc import cached_function
+from sage.structure.element import NumberFieldElement
+
 
 @cached_function
 def hilbert_class_polynomial(D, algorithm=None):
@@ -624,8 +626,6 @@ def is_cm_j_invariant(j, method='new'):
         True
     """
     # First we check that j is an algebraic number:
-    from sage.rings.number_field.number_field_element import NumberFieldElement
-    from sage.rings.number_field.number_field import NumberField
     if not isinstance(j, NumberFieldElement) and j not in QQ:
         raise NotImplementedError("is_cm_j_invariant() is only implemented for number field elements")
 
@@ -672,6 +672,8 @@ def is_cm_j_invariant(j, method='new'):
 
     K = j.parent()
     if h < K.absolute_degree():
+        from sage.rings.number_field.number_field import NumberField
+
         K = NumberField(jpol, 'j')
         j = K.gen()
 

src/sage/schemes/elliptic_curves/heegner.py

@@ -117,6 +117,7 @@
 from sage.rings.real_mpfr import RealField
 from sage.quadratic_forms.all import (BinaryQF,
                                       BinaryQF_reduced_representatives)
+from sage.structure.element import NumberFieldElement
 from sage.structure.sage_object import SageObject
 from sage.structure.richcmp import (richcmp_method, richcmp,
                                     richcmp_not_equal, rich_to_bool)
@@ -2683,7 +2684,7 @@ def __init__(self, N, D, c=ZZ(1), f=None, check=True):
                 elif isinstance(f, BinaryQF):
                     # convert from BinaryQF
                     f = tuple(f)
-                elif sage.rings.number_field.number_field_element.is_NumberFieldElement(f):
+                elif isinstance(f, NumberFieldElement):
                     # tau = number field element
                     g = f.minpoly()
                     if g.degree() != 2:

src/sage/structure/element.pxd

@@ -230,6 +230,9 @@ cdef class EuclideanDomainElement(PrincipalIdealDomainElement):
 cdef class FieldElement(CommutativeRingElement):
     cpdef _floordiv_(self, other)
 
+cdef class NumberFieldElement(FieldElement):
+    pass
+
 cdef class AlgebraElement(RingElement):
     pass
 

src/sage/structure/element.pyx

@@ -46,6 +46,7 @@ abstract base classes.
                                 PrincipalIdealDomainElement
                                     EuclideanDomainElement
                         FieldElement
+                            NumberFieldElement
                         CommutativeAlgebraElement
                         Expression
                     AlgebraElement
@@ -4263,6 +4264,29 @@ cdef class FieldElement(CommutativeRingElement):
             other = self.parent()(other)
         return bool(self) or other.is_zero()
 
+
+cdef class NumberFieldElement(FieldElement):
+    r"""
+    Abstract base class for :class:`~sage.rings.number_field.number_field_element.NumberFieldElement`
+
+    This class is defined for the purpose of :func:`isinstance` tests.  It should not be
+    instantiated.
+
+    EXAMPLES::
+
+        sage: k.<a> = NumberField(x^3 + x + 1)
+        sage: isinstance(a, sage.structure.element.NumberFieldElement)
+        True
+
+    By design, there is a unique direct subclass::
+
+        sage: len(sage.structure.element.NumberFieldElement.__subclasses__()) <= 1
+        True
+    """
+
+    pass
+
+
 def is_AlgebraElement(x):
     """
     Return ``True`` if x is of type AlgebraElement.

src/sage/symbolic/expression_conversions.py

@@ -20,10 +20,9 @@
 
 from sage.rings.rational_field import QQ
 from sage.symbolic.ring import SR
-from sage.structure.element import Expression
+from sage.structure.element import Expression, NumberFieldElement
 from sage.functions.all import exp
 from sage.symbolic.operators import arithmetic_operators, relation_operators, FDerivativeOperator, add_vararg, mul_vararg
-from sage.rings.number_field.number_field_element_quadratic import NumberFieldElement_gaussian
 from sage.rings.universal_cyclotomic_field import UniversalCyclotomicField
 
 
@@ -441,9 +440,10 @@ def pyobject(self, ex, obj):
             sage: ii.pyobject(pi, pi.pyobject())
             'Pi'
         """
-        if (self.interface.name() in ['pari', 'gp'] and
-            isinstance(obj, NumberFieldElement_gaussian)):
-            return repr(obj)
+        if (self.interface.name() in ['pari', 'gp'] and isinstance(obj, NumberFieldElement)):
+            from sage.rings.number_field.number_field_element_quadratic import NumberFieldElement_gaussian
+            if isinstance(obj, NumberFieldElement_gaussian):
+                return repr(obj)
         try:
             return getattr(obj, self.name_init)()
         except AttributeError:
@@ -1020,10 +1020,13 @@ def pyobject(self, ex, obj):
         """
         try:
             result = getattr(obj, self.name_init)()
-            if isinstance(obj, NumberFieldElement_gaussian):
-                return "((%s)::EXPR COMPLEX INT)" % result
         except AttributeError:
             result = repr(obj)
+        else:
+            if isinstance(obj, NumberFieldElement):
+                from sage.rings.number_field.number_field_element_quadratic import NumberFieldElement_gaussian
+                if isinstance(obj, NumberFieldElement_gaussian):
+                    return "((%s)::EXPR COMPLEX INT)" % result
         return "((%s)::EXPR INT)" % result
 
     def symbol(self, ex):