sage.rings: Break an import cycle

Author: Matthias Koeppe

src/sage/rings/rational.pyx

@@ -87,8 +87,26 @@ from sage.categories.morphism cimport Morphism
 from sage.categories.map cimport Map
 
 
-import sage.rings.real_mpfr
-import sage.rings.real_double
+RealNumber_classes = ()
+
+def _register_real_number_class(cls):
+    r"""
+    Register ``cls``.
+
+    This is called by ``sage.rings.real_mpfr``, to avoid a cyclic import.
+    """
+    global RealNumber_classes
+    RealNumber_classes += (cls,)
+
+
+RealDouble_classes = (float,)
+try:
+    from sage.rings.real_double import RealDoubleElement
+    RealDouble_classes += (RealDoubleElement,)
+except ImportError:
+    pass
+
+
 from libc.stdint cimport uint64_t
 from sage.libs.gmp.binop cimport mpq_add_z, mpq_mul_z, mpq_div_zz
 

src/sage/rings/real_lazy.pyx

@@ -50,12 +50,16 @@ from sage.rings.integer import Integer
 cdef QQ, RR, CC, RealField, ComplexField
 from sage.rings.rational_field import QQ
 
-try:
-    from sage.rings.real_mpfr import RR, RealField
-    from sage.rings.complex_mpfr import ComplexField
-    from sage.rings.cc import CC
-except ImportError:
-    pass
+cdef late_import():
+    global RR, CC, RealField, ComplexField
+    if CC is not None:
+        return
+    try:
+        from sage.rings.real_mpfr import RR, RealField
+        from sage.rings.complex_mpfr import ComplexField
+        from sage.rings.cc import CC
+    except ImportError:
+        pass
 
 cdef _QQx = None
 
@@ -1611,6 +1615,9 @@ cdef class LazyAlgebraic(LazyFieldElement):
         if self._poly.degree() == 2:
             c, b, a = self._poly.list()
             self._quadratic_disc = b*b - 4*a*c
+
+        late_import()
+
         if isinstance(parent, RealLazyField_class):
             if not self._poly.number_of_real_roots():
                 raise ValueError("%s has no real roots" % self._poly)

src/sage/rings/real_mpfr.pyx

@@ -6014,6 +6014,11 @@ cdef class int_toRR(Map):
         return y
 
 
+# Hook into Rational
+from sage.rings.rational import _register_real_number_class
+_register_real_number_class(RealNumber)
+
+
 # Support Python's numbers abstract base class
 import numbers
 numbers.Real.register(RealNumber)