Replace some imports of NumberFieldElement classes by ABC

Author: Matthias Koeppe

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/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/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 @@
                             PolynomialRing)
 
 from sage.misc.cachefunc import cached_function
+from sage.structure.element import NumberFieldElement
+
 
 @cached_function
 def hilbert_class_polynomial(D, algorithm=None):
@@ -623,7 +625,6 @@ def is_cm_j_invariant(j, method='new'):
         True
     """
     # First we check that j is an algebraic number:
-    from sage.rings.all import NumberFieldElement, NumberField
     if not isinstance(j, NumberFieldElement) and j not in QQ:
         raise NotImplementedError("is_cm_j_invariant() is only implemented for number field elements")
 
@@ -670,6 +671,8 @@ 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/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):