Trac #32660: Add sage.rings.abc.{AlgebraicField,...,NumberField_quadratic}, deprecate is_AlgebraicField, ..., is_CyclotomicField, is_QuadraticField

Part of meta-ticket #32414.

URL: https://trac.sagemath.org/32660
Reported by: mkoeppe
Ticket author(s): Matthias Koeppe
Reviewer(s): Jonathan Kliem

Author: Release Manager

src/sage/combinat/root_system/coxeter_type.py

@@ -21,12 +21,12 @@
 from sage.misc.cachefunc import cached_method
 from sage.misc.classcall_metaclass import ClasscallMetaclass
 from sage.combinat.root_system.cartan_type import CartanType
+import sage.rings.abc
 from sage.matrix.args import SparseEntry
 from sage.matrix.all import Matrix
 from sage.symbolic.ring import SR
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.structure.sage_object import SageObject
-from sage.rings.number_field.number_field import is_QuadraticField
 
 
 class CoxeterType(SageObject, metaclass=ClasscallMetaclass):
@@ -391,7 +391,7 @@ def val(x):
                     return (E(2*x) + ~E(2*x)) / R(-2)
                 else:
                     return R(x)
-        elif is_QuadraticField(R):
+        elif isinstance(R, sage.rings.abc.NumberField_quadratic):
 
             def val(x):
                 if x > -1:

src/sage/groups/matrix_gps/coxeter_group.py

@@ -27,10 +27,11 @@
 from sage.matrix.args import SparseEntry
 from sage.matrix.matrix_space import MatrixSpace
 
+import sage.rings.abc
 from sage.rings.integer_ring import ZZ
 from sage.rings.infinity import infinity
 from sage.rings.universal_cyclotomic_field import UniversalCyclotomicField
-from sage.rings.number_field.number_field import QuadraticField, is_QuadraticField
+from sage.rings.number_field.number_field import QuadraticField
 
 from sage.misc.cachefunc import cached_method
 
@@ -280,7 +281,7 @@ def val(x):
                     return 2
                 else:
                     return E(2 * x) + ~E(2 * x)
-        elif is_QuadraticField(base_ring):
+        elif isinstance(base_ring, sage.rings.abc.NumberField_quadratic):
 
             def val(x):
                 if x == -1:

src/sage/groups/misc_gps/argument_groups.py

@@ -735,9 +735,9 @@ def _element_constructor_(self, data, exponent=None, **kwds):
             zeta2^5
         """
         from sage.groups.generic import discrete_log
+        import sage.rings.abc
         from sage.rings.asymptotic.misc import combine_exceptions
         from sage.rings.rational_field import QQ
-        from sage.rings.number_field.number_field import NumberField_cyclotomic
 
         if exponent is None:
             if isinstance(data, int) and data == 0:
@@ -769,7 +769,7 @@ def _element_constructor_(self, data, exponent=None, **kwds):
                 elif isinstance(P, UnitCircleGroup):
                     exponent = data.exponent
 
-                elif isinstance(P, NumberField_cyclotomic):
+                elif isinstance(P, sage.rings.abc.NumberField_cyclotomic):
                     zeta = P.gen()
                     n = zeta.multiplicative_order()
                     try:

src/sage/interfaces/polymake.py

@@ -332,8 +332,10 @@ def convert(y):
             r.__sage_dict = z # do this to avoid having the entries of the list be garbage collected
             return r
 
-        from sage.rings.all import Integer, Rational, RDF
-        from sage.rings.number_field.number_field import is_QuadraticField
+        import sage.rings.abc
+        from sage.rings.integer import Integer
+        from sage.rings.rational import Rational
+        from sage.rings.real_double import RDF
 
         def to_str(x):
             if isinstance(x, list):
@@ -350,7 +352,7 @@ def to_str(x):
             except AttributeError:
                 pass
 
-            if is_QuadraticField(parent):
+            if isinstance(parent, sage.rings.abc.NumberField_quadratic):
                 return x._polymake_init_()
             try:
                 if x.parent().is_exact():

src/sage/matrix/matrix_space.py

@@ -255,7 +255,7 @@ def get_matrix_class(R, nrows, ncols, sparse, implementation):
                 if R.order() < matrix_modn_dense_double.MAX_MODULUS:
                     return matrix_modn_dense_double.Matrix_modn_dense_double
 
-            if sage.rings.number_field.number_field.is_CyclotomicField(R):
+            if isinstance(R, sage.rings.abc.NumberField_cyclotomic):
                 from . import matrix_cyclo_dense
                 return matrix_cyclo_dense.Matrix_cyclo_dense
 
@@ -338,7 +338,7 @@ def get_matrix_class(R, nrows, ncols, sparse, implementation):
             raise ValueError("'numpy' matrices are only available over RDF and CDF")
 
         if implementation == 'rational':
-            if sage.rings.number_field.number_field.is_CyclotomicField(R):
+            if isinstance(R, sage.rings.abc.NumberField_cyclotomic):
                 from . import matrix_cyclo_dense
                 return matrix_cyclo_dense.Matrix_cyclo_dense
             raise ValueError("'rational' matrices are only available over a cyclotomic field")

src/sage/modular/dirichlet.py

@@ -69,7 +69,6 @@
 from sage.categories.map import Map
 from sage.rings.rational_field import is_RationalField
 import sage.rings.abc
-from sage.rings.qqbar import is_AlgebraicField
 from sage.rings.ring import is_Ring
 
 from sage.misc.functional import round
@@ -1347,10 +1346,10 @@ def gauss_sum(self, a=1):
         m = G.modulus()
         if isinstance(K, sage.rings.abc.ComplexField):
             return self.gauss_sum_numerical(a=a)
-        elif is_AlgebraicField(K):
+        elif isinstance(K, sage.rings.abc.AlgebraicField):
             L = K
             zeta = L.zeta(m)
-        elif number_field.is_CyclotomicField(K) or is_RationalField(K):
+        elif isinstance(K, sage.rings.abc.NumberField_cyclotomic) or is_RationalField(K):
             chi = chi.minimize_base_ring()
             n = lcm(m, G.zeta_order())
             L = rings.CyclotomicField(n)
@@ -1427,11 +1426,11 @@ def gauss_sum_numerical(self, prec=53, a=1):
             def phi(t):
                 return t
             CC = K
-        elif is_AlgebraicField(K):
+        elif isinstance(K, sage.rings.abc.AlgebraicField):
             from sage.rings.complex_mpfr import ComplexField
             CC = ComplexField(prec)
             phi = CC.coerce_map_from(K)
-        elif number_field.is_CyclotomicField(K) or is_RationalField(K):
+        elif isinstance(K, sage.rings.abc.NumberField_cyclotomic) or is_RationalField(K):
             phi = K.complex_embedding(prec)
             CC = phi.codomain()
         else:
@@ -1650,7 +1649,7 @@ def kloosterman_sum_numerical(self, prec=53, a=1, b=0):
         """
         G = self.parent()
         K = G.base_ring()
-        if not (number_field.is_CyclotomicField(K) or is_RationalField(K)):
+        if not (isinstance(K, sage.rings.abc.NumberField_cyclotomic) or is_RationalField(K)):
             raise NotImplementedError("Kloosterman sums only currently implemented when the base ring is a cyclotomic field or QQ.")
         phi = K.complex_embedding(prec)
         CC = phi.codomain()

src/sage/rings/abc.pyx

@@ -2,6 +2,46 @@
 Abstract base classes for rings
 """
 
+class NumberField_quadratic(Field):
+    r"""
+    Abstract base class for :class:`~sage.rings.number_field.number_field.NumberField_quadratic`.
+    """
+
+    pass
+
+
+class NumberField_cyclotomic(Field):
+    r"""
+    Abstract base class for :class:`~sage.rings.number_field.number_field.NumberField_cyclotomic`.
+    """
+
+    pass
+
+
+class AlgebraicField_common(Field):
+    r"""
+    Abstract base class for :class:`~sage.rings.qqbar.AlgebraicField_common`.
+    """
+
+    pass
+
+
+class AlgebraicField(AlgebraicField_common):
+    r"""
+    Abstract base class for :class:`~sage.rings.qqbar.AlgebraicField`.
+    """
+
+    pass
+
+
+class AlgebraicRealField(AlgebraicField_common):
+    r"""
+    Abstract base class for :class:`~sage.rings.qqbar.AlgebraicRealField`.
+    """
+
+    pass
+
+
 cdef class RealField(Field):
     r"""
     Abstract base class for :class:`~sage.rings.real_mpfr.RealField_class`.

src/sage/rings/complex_mpfr.pyx

@@ -46,6 +46,7 @@ from sage.structure.parent_gens import ParentWithGens
 
 from sage.misc.sage_eval import sage_eval
 
+import sage.rings.abc
 from sage.arith.constants cimport LOG_TEN_TWO_PLUS_EPSILON
 from . import ring, infinity
 from .integer cimport Integer
@@ -64,7 +65,6 @@ gmpy2.import_gmpy2()
 
 # Some objects that are note imported at startup in order to break
 # circular imports
-NumberField_quadratic = None
 NumberFieldElement_quadratic = None
 AlgebraicNumber_base = None
 AlgebraicNumber = None
@@ -81,7 +81,6 @@ def late_import():
 
         sage: sage.rings.complex_mpfr.late_import()
     """
-    global NumberField_quadratic
     global NumberFieldElement_quadratic
     global AlgebraicNumber_base
     global AlgebraicNumber
@@ -92,7 +91,6 @@ def late_import():
     if NumberFieldElement_quadratic is None:
         import sage.rings.number_field.number_field
         import sage.rings.number_field.number_field_element_quadratic as nfeq
-        NumberField_quadratic = sage.rings.number_field.number_field.NumberField_quadratic
         NumberFieldElement_quadratic = nfeq.NumberFieldElement_quadratic
         import sage.rings.qqbar
         AlgebraicNumber_base = sage.rings.qqbar.AlgebraicNumber_base
@@ -528,7 +526,7 @@ class ComplexField_class(sage.rings.abc.ComplexField):
 
             late_import()
             if isinstance(x, NumberFieldElement_quadratic):
-                if isinstance(x.parent(), NumberField_quadratic) and list(x.parent().polynomial()) == [1, 0, 1]:
+                if isinstance(x.parent(), sage.rings.abc.NumberField_quadratic) and list(x.parent().polynomial()) == [1, 0, 1]:
                     (re, im) = list(x)
                     return ComplexNumber(self, re, im)
 

src/sage/rings/number_field/number_field.py

@@ -1041,10 +1041,17 @@ def is_QuadraticField(x):
     r"""
     Return True if x is of the quadratic *number* field type.
 
+    This function is deprecated. Use :func:`isinstance` with
+    :class:`~sage.rings.abc.NumberField_quadratic` instead.
+
     EXAMPLES::
 
         sage: from sage.rings.number_field.number_field import is_QuadraticField
         sage: is_QuadraticField(QuadraticField(5,'a'))
+        doctest:warning...
+        DeprecationWarning: is_QuadraticField is deprecated;
+        use isinstance(..., sage.rings.abc.NumberField_quadratic instead
+        See https://trac.sagemath.org/32660 for details.
         True
         sage: is_QuadraticField(NumberField(x^2 - 5, 'b'))
         True
@@ -1057,6 +1064,8 @@ def is_QuadraticField(x):
         sage: is_QuadraticField(GF(9,'a'))
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(32660, 'is_QuadraticField is deprecated; use isinstance(..., sage.rings.abc.NumberField_quadratic instead')
     return isinstance(x, NumberField_quadratic)
 
 
@@ -1229,10 +1238,17 @@ def is_CyclotomicField(x):
     number field that just happens to be isomorphic to a cyclotomic
     field.
 
+    This function is deprecated. Use :func:`isinstance` with
+    :class:`~sage.rings.abc.NumberField_cyclotomic` instead.
+
     EXAMPLES::
 
         sage: from sage.rings.number_field.number_field import is_CyclotomicField
         sage: is_CyclotomicField(NumberField(x^2 + 1,'zeta4'))
+        doctest:warning...
+        DeprecationWarning: is_CyclotomicField is deprecated;
+        use isinstance(..., sage.rings.abc.NumberField_cyclotomic instead
+        See https://trac.sagemath.org/32660 for details.
         False
         sage: is_CyclotomicField(CyclotomicField(4))
         True
@@ -1243,6 +1259,8 @@ def is_CyclotomicField(x):
         sage: is_CyclotomicField(7)
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(32660, 'is_CyclotomicField is deprecated; use isinstance(..., sage.rings.abc.NumberField_cyclotomic instead')
     return isinstance(x, NumberField_cyclotomic)
 
 
@@ -10346,7 +10364,7 @@ def _factor_univariate_polynomial(self, poly, **kwargs):
         return poly._factor_pari_helper(G)
 
 
-class NumberField_cyclotomic(NumberField_absolute):
+class NumberField_cyclotomic(NumberField_absolute, sage.rings.abc.NumberField_cyclotomic):
     """
     Create a cyclotomic extension of the rational field.
 
@@ -11249,7 +11267,7 @@ def is_isomorphic(self, other):
             sage: K.is_isomorphic(CyclotomicField(8))
             False
         """
-        if is_CyclotomicField(other):
+        if isinstance(other, NumberField_cyclotomic):
             return self.zeta_order() == other.zeta_order()
         return NumberField_generic.is_isomorphic(self, other)
 
@@ -11709,7 +11727,7 @@ def roots_of_unity(self):
         return v
 
 
-class NumberField_quadratic(NumberField_absolute):
+class NumberField_quadratic(NumberField_absolute, sage.rings.abc.NumberField_quadratic):
     r"""
     Create a quadratic extension of the rational field.