Running

sage -cython quadratic_numerical_approx.pyx 

gives a better error message :

$ sage -cython quadratic_numerical_approx.pyx 
Error compiling Cython file:
------------------------------------------------------------
...
include "sage/libs/ntl/decl.pxi"
^
------------------------------------------------------------

/home/labbe/Applications/sage-git/local/lib/python2.7/site-packages/sage/rings/number_field/number_field_element_quadratic.pxd:1:0:
 
'sage/libs/ntl/decl.pxi' not found


Error compiling Cython file:
------------------------------------------------------------
...
from sage.libs.gmp.mpz cimport *
from sage.libs.mpfr cimport *

from sage.rings.number_field.number_field_element_quadratic cimport 
NumberFieldElement_quadratic
^
------------------------------------------------------------

quadratic_numerical_approx.pyx:4:0: 'NumberFieldElement_quadratic.pxd' not 
found

Error compiling Cython file:
------------------------------------------------------------
...
from sage.libs.gmp.mpz cimport *
from sage.libs.mpfr cimport *

from sage.rings.number_field.number_field_element_quadratic cimport 
NumberFieldElement_quadratic
                                                                   ^
------------------------------------------------------------

quadratic_numerical_approx.pyx:4:68: Name 'NumberFieldElement_quadratic' 
not declared in module 
'sage.rings.number_field.number_field_element_quadratic'

Error compiling Cython file:
------------------------------------------------------------
...

from sage.rings.number_field.number_field_element_quadratic cimport 
NumberFieldElement_quadratic

from sage.rings.real_mpfr cimport RealNumber, RealField_class

def quad_nf_element_numerical_approx(NumberFieldElement_quadratic x,
                                    ^
------------------------------------------------------------

quadratic_numerical_approx.pyx:8:37: 'NumberFieldElement_quadratic' is not 
a type identifier

Error compiling Cython file:
------------------------------------------------------------
...
    r"""
    Return an approximation of the quadratic element ``x`` in the given real
    field ``R``.
    """
    cdef RealNumber y = R._new()
    mpfr_set_z(y.value, x.D.value, R.rnd)
                          ^
------------------------------------------------------------

quadratic_numerical_approx.pyx:15:27: Cannot convert Python object to 
'__mpz_struct *'

Error compiling Cython file:
------------------------------------------------------------
...
    field ``R``.
    """
    cdef RealNumber y = R._new()
    mpfr_set_z(y.value, x.D.value, R.rnd)
    mpfr_sqrt(y.value, y.value, R.rnd)
    mpfr_mul_z(y.value, y.value, x.b, R.rnd)
                                 ^
------------------------------------------------------------

quadratic_numerical_approx.pyx:17:34: Cannot convert Python object to 
'__mpz_struct *'

Error compiling Cython file:
------------------------------------------------------------
...
    """
    cdef RealNumber y = R._new()
    mpfr_set_z(y.value, x.D.value, R.rnd)
    mpfr_sqrt(y.value, y.value, R.rnd)
    mpfr_mul_z(y.value, y.value, x.b, R.rnd)
    mpfr_add_z(y.value, y.value, x.a, R.rnd)
                                 ^
------------------------------------------------------------

quadratic_numerical_approx.pyx:18:34: Cannot convert Python object to 
'__mpz_struct *'

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