sage.rings.number_field.number_field_element_base: New

Author: Matthias Koeppe

src/sage/interfaces/maxima_lib.py

@@ -1165,7 +1165,7 @@ def reduce_load_MaximaLib():
 import sage.symbolic.expression
 import sage.symbolic.integration.integral
 
-from sage.structure.element import NumberFieldElement
+from sage.rings.number_field.number_field_element_base import NumberFieldElement_base
 from sage.symbolic.operators import FDerivativeOperator, add_vararg, mul_vararg
 
 car=EclObject("car")
@@ -1525,7 +1525,7 @@ 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, NumberFieldElement):
+    elif isinstance(obj, NumberFieldElement_base):
         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()

src/sage/rings/finite_rings/residue_field.pyx

@@ -160,7 +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, NumberFieldElement
+from sage.rings.number_field.number_field_element_base import NumberFieldElement_base
+from sage.structure.element cimport Element
 
 from sage.rings.number_field.number_field_ideal import is_NumberFieldIdeal
 
@@ -294,7 +295,7 @@ class ResidueFieldFactory(UniqueFactory):
             if not is_Ideal(p):
                 if isinstance(p, (int, Integer, Rational)):
                     p = ZZ.ideal(p)
-                elif isinstance(p, NumberFieldElement):
+                elif isinstance(p, NumberFieldElement_base):
                     if p.parent().is_field():
                         p = p.parent().ring_of_integers().ideal(p)
                     else:

src/sage/rings/integer_ring.pyx

@@ -58,8 +58,9 @@ import sage.libs.pari.all
 import sage.rings.ideal
 from sage.categories.basic import EuclideanDomains
 from sage.categories.infinite_enumerated_sets import InfiniteEnumeratedSets
+from sage.rings.number_field.number_field_element_base import NumberFieldElement_base
 from sage.structure.coerce cimport is_numpy_type
-from sage.structure.element cimport parent, NumberFieldElement
+from sage.structure.element cimport parent
 from sage.structure.parent_gens import ParentWithGens
 from sage.structure.parent cimport Parent
 from sage.structure.richcmp cimport rich_to_bool
@@ -414,7 +415,7 @@ cdef class IntegerRing_class(PrincipalIdealDomain):
         if x in self:
             return self
 
-        if isinstance(x, NumberFieldElement):
+        if isinstance(x, NumberFieldElement_base):
             K, from_K = parent(x).subfield(x)
             return K.order(K.gen())
 

src/sage/rings/number_field/number_field_element.pxd

@@ -1,9 +1,8 @@
 cimport sage.structure.element
 from sage.libs.gmp.types cimport mpz_t
 from sage.rings.integer cimport Integer
+from sage.rings.number_field.number_field_element_base cimport NumberFieldElement_base
 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

src/sage/rings/number_field/number_field_element.pyx

@@ -5,7 +5,7 @@
 # distutils: extra_link_args = NTL_LIBEXTRA
 # distutils: language = c++
 """
-Number Field Elements
+Number field elements (implementation using NTL)
 
 AUTHORS:
 

src/sage/rings/number_field/number_field_element_base.pxd

@@ -0,0 +1,5 @@
+from sage.structure.element cimport FieldElement
+
+
+cdef class NumberFieldElement_base(FieldElement):
+    pass

src/sage/rings/number_field/number_field_element_base.pyx

@@ -0,0 +1,33 @@
+r"""
+Number field elements (abstract base class)
+"""
+
+# ****************************************************************************
+#       Copyright (C) 2023 Matthias Koeppe
+#
+#  Distributed under the terms of the GNU General Public License (GPL)
+#  as published by the Free Software Foundation; either version 2 of
+#  the License, or (at your option) any later version.
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
+
+cdef class NumberFieldElement_base(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.rings.number_field.number_field_element_base.NumberFieldElement_base)
+        True
+
+    By design, there is a unique direct subclass::
+
+        sage: len(sage.rings.number_field.number_field_element_base.NumberFieldElement_base.__subclasses__()) <= 1
+        True
+    """
+
+    pass

src/sage/rings/universal_cyclotomic_field.py

@@ -167,7 +167,7 @@
 
 from sage.structure.richcmp import rich_to_bool
 from sage.structure.unique_representation import UniqueRepresentation
-from sage.structure.element import FieldElement, parent, NumberFieldElement
+from sage.structure.element import FieldElement, parent
 
 from sage.structure.coerce import py_scalar_to_element
 from sage.categories.morphism import Morphism
@@ -177,6 +177,7 @@
 from sage.rings.rational import Rational
 
 from sage.rings.integer_ring import ZZ
+from sage.rings.number_field.number_field_element_base import NumberFieldElement_base
 from sage.rings.rational_field import QQ
 from sage.rings.infinity import Infinity
 from sage.rings.qqbar import AA, QQbar
@@ -1538,7 +1539,7 @@ def _element_constructor_(self, elt):
         import sage.rings.abc
         P = parent(elt)
         if isinstance(P, sage.rings.abc.NumberField_cyclotomic):
-            if isinstance(elt, NumberFieldElement):
+            if isinstance(elt, NumberFieldElement_base):
                 from sage.rings.number_field.number_field import CyclotomicField
                 n = P.gen().multiplicative_order()
                 elt = CyclotomicField(n)(elt)

src/sage/schemes/elliptic_curves/cm.py

@@ -42,7 +42,7 @@
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 
 from sage.misc.cachefunc import cached_function
-from sage.structure.element import NumberFieldElement
+from sage.rings.number_field.number_field_element_base import NumberFieldElement_base
 
 
 @cached_function
@@ -626,7 +626,7 @@ def is_cm_j_invariant(j, method='new'):
         True
     """
     # First we check that j is an algebraic number:
-    if not isinstance(j, NumberFieldElement) and j not in QQ:
+    if not isinstance(j, NumberFieldElement_base) and j not in QQ:
         raise NotImplementedError("is_cm_j_invariant() is only implemented for number field elements")
 
     # for j in ZZ we have a lookup-table:

src/sage/schemes/elliptic_curves/heegner.py

@@ -117,7 +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.rings.number_field.number_field_element_base import NumberFieldElement_base
 from sage.structure.sage_object import SageObject
 from sage.structure.richcmp import (richcmp_method, richcmp,
                                     richcmp_not_equal, rich_to_bool)
@@ -2684,7 +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 isinstance(f, NumberFieldElement):
+                elif isinstance(f, NumberFieldElement_base):
                     # tau = number field element
                     g = f.minpoly()
                     if g.degree() != 2: