Trac #32641: Decentralize sage.rings.numbers_abc

For the modularization, it's better to do the numbers ABC registration
in the individual implementation modules.

We keep the module `sage.rings.numbers_abc` just for the doctests.

URL: https://trac.sagemath.org/32641
Reported by: mkoeppe
Ticket author(s): Matthias Koeppe
Reviewer(s): Travis Scrimshaw

src/sage/rings/complex_double.pyx

@@ -2660,3 +2660,8 @@ cdef inline ComplexDoubleElement ComplexDoubleElement_from_doubles(double re, do
     z = <ComplexDoubleElement>ComplexDoubleElement.__new__(ComplexDoubleElement)
     GSL_SET_COMPLEX(&z._complex, re, im)
     return z
+
+
+# Support Python's numbers abstract base class
+import numbers
+numbers.Complex.register(ComplexDoubleElement)

src/sage/rings/complex_mpc.pyx

@@ -2575,3 +2575,8 @@ cdef class CCtoMPC(Map):
         y = (<MPComplexField_class>self.codomain())._new()
         mpc_set_fr_fr(y.value, (<ComplexNumber>z).__re, (<ComplexNumber>z).__im, rnd)
         return y
+
+
+# Support Python's numbers abstract base class
+import numbers
+from sage.rings.complex_mpc import MPComplexNumber

src/sage/rings/complex_mpfr.pyx

@@ -3626,3 +3626,8 @@ def _format_complex_number(real, imag, format_spec):
                              "complex format specifier")
         result = format(result, align + width)
     return result
+
+
+# Support Python's numbers abstract base class
+import numbers
+numbers.Complex.register(ComplexNumber)

src/sage/rings/integer.pyx

@@ -7564,3 +7564,8 @@ cdef double mpz_get_d_nearest(mpz_t x) except? -648555075988944.5:
     if resultsign < 0:
         d = -d
     return ldexp(d, shift)
+
+
+# Support Python's numbers abstract base class
+import numbers
+numbers.Integral.register(Integer)

src/sage/rings/numbers_abc.py

@@ -14,8 +14,6 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
-import numbers
-
 
 def register_sage_classes():
     """
@@ -65,23 +63,5 @@ def register_sage_classes():
         sage: isscalar(4/17)
         True
     """
-    from sage.rings.integer import Integer
-    from sage.rings.rational import Rational
-    from sage.rings.real_mpfr import RealNumber
-    from sage.rings.real_double import RealDoubleElement
-    from sage.rings.complex_mpfr import ComplexNumber
-    from sage.rings.complex_double import ComplexDoubleElement
-    from sage.rings.complex_mpc import MPComplexNumber
-    from sage.rings.qqbar import AlgebraicReal, AlgebraicNumber
-
-    numbers.Integral.register(Integer)
-    numbers.Rational.register(Rational)
-    numbers.Real.register(RealNumber)
-    numbers.Real.register(RealDoubleElement)
-    numbers.Real.register(AlgebraicReal)
-    numbers.Complex.register(ComplexNumber)
-    numbers.Complex.register(MPComplexNumber)
-    numbers.Complex.register(ComplexDoubleElement)
-    numbers.Complex.register(AlgebraicNumber)
-
-register_sage_classes()
+    from sage.misc.superseded import deprecation
+    deprecation(32641, "register_sage_classes is a deprecated no-op")

src/sage/rings/qqbar.py

@@ -8574,3 +8574,9 @@ def get_AA_golden_ratio():
         AA_golden_ratio_generator = AlgebraicGenerator(AA_golden_ratio_nf, ANRoot(AAPoly.gen()**2 - AAPoly.gen() - 1, RIF(1.618, 1.6181)))
         AA_golden_ratio = AlgebraicReal(ANExtensionElement(AA_golden_ratio_generator, AA_golden_ratio_nf.gen()))
     return AA_golden_ratio
+
+
+# Support Python's numbers abstract base class
+import numbers
+numbers.Real.register(AlgebraicReal)
+numbers.Complex.register(AlgebraicNumber)

src/sage/rings/rational.pyx

@@ -4297,3 +4297,8 @@ cdef class long_to_Q(Morphism):
             'Native'
         """
         return "Native"
+
+
+# Support Python's numbers abstract base class
+import numbers
+numbers.Rational.register(Rational)

src/sage/rings/real_double.pyx

@@ -2943,3 +2943,8 @@ cdef double_repr(double x):
     if v < 0:
         return "-infinity"
     return "NaN"
+
+
+# Support Python's numbers abstract base class
+import numbers
+numbers.Real.register(RealDoubleElement)

src/sage/rings/real_mpfr.pyx

@@ -6122,3 +6122,8 @@ def create_RealField(*args, **kwds):
     deprecation(24511, "Please import create_RealField from sage.rings.real_field")
     from sage.rings.real_field import create_RealField as cr
     return cr(*args, **kwds)
+
+
+# Support Python's numbers abstract base class
+import numbers
+numbers.Real.register(RealNumber)