erf of complex arguments

[vbraun]

The erf function doesn't work for complex arguments, even though we use Pari and Pari does support it. This is also annoying because maxima sometimes returns erf(complex argument) in integrations:

sage: integrate(sin(x)*(x^(1/2)),x,0,1)
-1/8*((I + 1)*sqrt(2)*erf((1/2*I - 1/2)*sqrt(2)) + (I - 1)*sqrt(2)*erf((1/2*I + 1/2)*sqrt(2)))*sqrt(pi) - cos(1)
sage: _.n()
ERROR: An unexpected error occurred while tokenizing input
The following traceback may be corrupted or invalid
The error message is: ('EOF in multi-line statement', (1111, 0))

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/home/vbraun/opt/sage-weak/sage-4.8.alpha5/<ipython console> in <module>()

/home/vbraun/opt/sage-4.8.alpha4/local/lib/python2.6/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression._numerical_approx (sage/symbolic/expression.cpp:18004)()

/home/vbraun/opt/sage-4.8.alpha4/local/lib/python2.6/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression._convert (sage/symbolic/expression.cpp:5089)()

/home/vbraun/opt/sage-4.8.alpha4/local/lib/python2.6/site-packages/sage/functions/other.pyc in _evalf_(self, x, parent)
     79         if prec > 53:
     80             raise NotImplementedError, "erf not implemented for precision higher than 53"
---> 81         return parent(1 - pari(float(x)).erfc())
     82         
     83     def _derivative_(self, x, diff_param=None):

/home/vbraun/opt/sage-4.8.alpha4/local/lib/python2.6/site-packages/sage/rings/complex_number.so in sage.rings.complex_number.ComplexNumber.__float__ (sage/rings/complex_number.c:7501)()

TypeError: Unable to convert -0.707106781186547 + 0.707106781186547*I to float; use abs() or real_part() as desired

See #11948 for a better solution.

[vbraun]

Initial patch

[dimpase]

Replying to vbraun:

it works on MacOSX, and otherwise makes sense, too.

[jdemeyer]

Already fixed by #11948, so closing as "duplicate".