Trac #32566: sage.rings.abc

This new module will provide abstract base classes for the purpose of
`isinstance` and `issubclass` testing.  This helps with modularization
(#32432).

In this ticket, we add `RealField`, `RealDoubleField`, `ComplexField`,
`ComplexDoubleField`, which are in 1:1 correspondence to the
implementation classes `RealField_class`, `RealDoubleField_class`,
`ComplexField_class`, `ComplexDoubleField_class`.

To illustrate the use of these classes, we convert some uses of `is_...`
functions to `isinstance` with the new base classes.

Related:
- https://groups.google.com/g/sage-devel/c/T0A4JCOg9DY/m/q6WKsI1yBAAJ
(Sep 2021)

Part of meta-ticket #32414.

URL: https://trac.sagemath.org/32566
Reported by: mkoeppe
Ticket author(s): Matthias Koeppe
Reviewer(s): Jonathan Kliem

src/sage/rings/abc.pxd

@@ -0,0 +1,20 @@
+from .ring cimport Field
+
+cdef class RealField(Field):
+
+    pass
+
+
+cdef class RealDoubleField(Field):
+
+    pass
+
+
+cdef class ComplexField(Field):
+
+    pass
+
+
+cdef class ComplexDoubleField(Field):
+
+    pass

src/sage/rings/abc.pyx

@@ -0,0 +1,34 @@
+"""
+Abstract base classes for rings
+"""
+
+cdef class RealField(Field):
+    r"""
+    Abstract base class for :class:`~sage.rings.real_mpfr.RealField_class`.
+    """
+
+    pass
+
+
+cdef class RealDoubleField(Field):
+    r"""
+    Abstract base class for :class:`~sage.rings.real_double.RealDoubleField_class`.
+    """
+
+    pass
+
+
+cdef class ComplexField(Field):
+    r"""
+    Abstract base class for :class:`~sage.rings.complex_mpfr.ComplexField_class`.
+    """
+
+    pass
+
+
+cdef class ComplexDoubleField(Field):
+    r"""
+    Abstract base class for :class:`~sage.rings.complex_double.ComplexDoubleField_class`.
+    """
+
+    pass

src/sage/rings/complex_double.pxd

@@ -2,9 +2,10 @@ from sage.libs.gsl.types cimport gsl_complex
 
 cimport sage.structure.element
 cimport sage.rings.ring
+cimport sage.rings.abc
 
 
-cdef class ComplexDoubleField_class(sage.rings.ring.Field):
+cdef class ComplexDoubleField_class(sage.rings.abc.ComplexDoubleField):
     pass
 
 

src/sage/rings/complex_double.pyx

@@ -126,7 +126,7 @@ def is_ComplexDoubleField(x):
     return isinstance(x, ComplexDoubleField_class)
 
 
-cdef class ComplexDoubleField_class(sage.rings.ring.Field):
+cdef class ComplexDoubleField_class(sage.rings.abc.ComplexDoubleField):
     """
     An approximation to the field of complex numbers using double
     precision floating point numbers. Answers derived from calculations

src/sage/rings/complex_mpfr.pyx

@@ -202,7 +202,7 @@ def ComplexField(prec=53, names=None):
     return C
 
 
-class ComplexField_class(ring.Field):
+class ComplexField_class(sage.rings.abc.ComplexField):
     """
     An approximation to the field of complex numbers using floating
     point numbers with any specified precision. Answers derived from

src/sage/rings/polynomial/polynomial_element.pyx

@@ -51,7 +51,7 @@ TESTS::
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-cdef is_FractionField, is_RealField, is_ComplexField
+cdef is_FractionField
 cdef ZZ, QQ, RR, CC, RDF, CDF
 
 cimport cython
@@ -84,13 +84,14 @@ from sage.structure.richcmp cimport (richcmp, richcmp_item,
 from sage.interfaces.singular import singular as singular_default, is_SingularElement
 from sage.libs.all import pari, pari_gen, PariError
 
-from sage.rings.real_mpfr import RealField, is_RealField, RR
+cimport sage.rings.abc
+from sage.rings.real_mpfr import RealField, RR
 
-from sage.rings.complex_mpfr import is_ComplexField, ComplexField
+from sage.rings.complex_mpfr import ComplexField
 CC = ComplexField()
 
-from sage.rings.real_double import is_RealDoubleField, RDF
-from sage.rings.complex_double import is_ComplexDoubleField, CDF
+from sage.rings.real_double import RDF
+from sage.rings.complex_double import CDF
 from sage.rings.real_mpfi import is_RealIntervalField
 
 from sage.structure.coerce cimport coercion_model
@@ -7852,25 +7853,23 @@ cdef class Polynomial(CommutativeAlgebraElement):
 
         late_import()
 
-        input_fp = (is_RealField(K)
-                    or is_ComplexField(K)
-                    or is_RealDoubleField(K)
-                    or is_ComplexDoubleField(K))
-        output_fp = (is_RealField(L)
-                     or is_ComplexField(L)
-                     or is_RealDoubleField(L)
-                     or is_ComplexDoubleField(L))
-        input_complex = (is_ComplexField(K)
-                         or is_ComplexDoubleField(K))
-        output_complex = (is_ComplexField(L)
-                          or is_ComplexDoubleField(L))
+        input_fp = isinstance(K, (sage.rings.abc.RealField,
+                                  sage.rings.abc.ComplexField,
+                                  sage.rings.abc.RealDoubleField,
+                                  sage.rings.abc.ComplexDoubleField))
+        output_fp = isinstance(L, (sage.rings.abc.RealField,
+                                  sage.rings.abc.ComplexField,
+                                  sage.rings.abc.RealDoubleField,
+                                  sage.rings.abc.ComplexDoubleField))
+        input_complex = isinstance(K, (sage.rings.abc.ComplexField, sage.rings.abc.ComplexDoubleField))
+        output_complex = isinstance(L, (sage.rings.abc.ComplexField, sage.rings.abc.ComplexDoubleField))
         input_gaussian = (isinstance(K, NumberField_quadratic)
                           and list(K.polynomial()) == [1, 0, 1])
 
         if input_fp and output_fp:
             # allow for possibly using a fast but less reliable
             # floating point algorithm from numpy
-            low_prec = is_RealDoubleField(K) or is_ComplexDoubleField(K)
+            low_prec = isinstance(K, (sage.rings.abc.RealDoubleField, sage.rings.abc.ComplexDoubleField))
             if algorithm is None:
                 if low_prec:
                     algorithm = 'either'
@@ -7883,8 +7882,7 @@ cdef class Polynomial(CommutativeAlgebraElement):
             # We should support GSL, too.  We could also support PARI's
             # old Newton-iteration algorithm.
 
-            input_arbprec = (is_RealField(K) or
-                             is_ComplexField(K))
+            input_arbprec = isinstance(K, (sage.rings.abc.RealField, sage.rings.abc.ComplexField))
 
             if algorithm == 'numpy' or algorithm == 'either':
                 if K.prec() > 53 and L.prec() > 53:
@@ -8022,7 +8020,7 @@ cdef class Polynomial(CommutativeAlgebraElement):
                 # If we want the complex roots, and the input is not
                 # floating point, we convert to a real polynomial
                 # (except when the input coefficients are Gaussian rationals).
-                if is_ComplexDoubleField(L):
+                if isinstance(L, sage.rings.abc.ComplexDoubleField):
                     real_field = RDF
                 else:
                     real_field = RealField(L.prec())
@@ -8190,7 +8188,7 @@ cdef class Polynomial(CommutativeAlgebraElement):
             True
         """
         K = self.base_ring()
-        if is_RealField(K) or is_RealDoubleField(K):
+        if isinstance(K, (sage.rings.abc.RealField, sage.rings.abc.RealDoubleField)):
             return self.roots(multiplicities=False)
 
         return self.roots(ring=RR, multiplicities=False)
@@ -8232,11 +8230,11 @@ cdef class Polynomial(CommutativeAlgebraElement):
             True
         """
         K = self.base_ring()
-        if is_RealField(K):
+        if isinstance(K, sage.rings.abc.RealField):
             return self.roots(ring=ComplexField(K.prec()), multiplicities=False)
-        if is_RealDoubleField(K):
+        if isinstance(K, sage.rings.abc.RealDoubleField):
             return self.roots(ring=CDF, multiplicities=False)
-        if is_ComplexField(K) or is_ComplexDoubleField(K):
+        if isinstance(K, (sage.rings.abc.ComplexField, sage.rings.abc.ComplexDoubleField)):
             return self.roots(multiplicities=False)
 
         return self.roots(ring=CC, multiplicities=False)

src/sage/rings/real_double.pxd

@@ -1,7 +1,8 @@
 from sage.structure.element cimport RingElement, ModuleElement, Element, FieldElement
 from sage.rings.ring cimport Field
+cimport sage.rings.abc
 
-cdef class RealDoubleField_class(Field):
+cdef class RealDoubleField_class(sage.rings.abc.RealDoubleField):
     cdef _new_c(self, double value)
 
 cdef class RealDoubleElement(FieldElement):

src/sage/rings/real_double.pyx

@@ -87,7 +87,7 @@ def is_RealDoubleField(x):
     """
     return isinstance(x, RealDoubleField_class)
 
-cdef class RealDoubleField_class(Field):
+cdef class RealDoubleField_class(sage.rings.abc.RealDoubleField):
     """
     An approximation to the field of real numbers using double
     precision floating point numbers. Answers derived from calculations

src/sage/rings/real_mpfr.pxd

@@ -1,13 +1,14 @@
 from sage.libs.mpfr.types cimport mpfr_rnd_t, mpfr_t
 
 cimport sage.rings.ring
+cimport sage.rings.abc
 cimport sage.structure.element
 from cypari2.types cimport GEN
 from sage.libs.mpfr.types cimport mpfr_prec_t
 
 cdef class RealNumber(sage.structure.element.RingElement)  # forward decl
 
-cdef class RealField_class(sage.rings.ring.Field):
+cdef class RealField_class(sage.rings.abc.RealField):
     cdef mpfr_prec_t __prec
     cdef bint sci_not
     cdef mpfr_rnd_t rnd

src/sage/rings/real_mpfr.pyx

@@ -454,7 +454,7 @@ cpdef RealField(mpfr_prec_t prec=53, int sci_not=0, rnd=MPFR_RNDN):
         return R
 
 
-cdef class RealField_class(sage.rings.ring.Field):
+cdef class RealField_class(sage.rings.abc.RealField):
     """
     An approximation to the field of real numbers using floating point
     numbers with any specified precision. Answers derived from