#12237: erf of complex arguments
-------------------------+--------------------------------------------------
Reporter: vbraun | Owner: jason, jkantor
Type: defect | Status: new
Priority: major | Milestone: sage-4.8
Component: numerical | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author: Volker Braun
Merged: | Dependencies:
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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
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12237>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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