sage.structure.element.NumberFieldElement: New ABC

Author: Matthias Koeppe

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

@@ -190,7 +190,7 @@ 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.
 

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: 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.