#8568: can not simplify derivative of erf
------------------------+---------------------------------------------------
   Reporter:  gmcmanus  |       Owner:  burcin
       Type:  defect    |      Status:  new   
   Priority:  major     |   Milestone:        
  Component:  calculus  |    Keywords:        
     Author:            |    Upstream:  N/A   
   Reviewer:            |      Merged:        
Work_issues:            |  
------------------------+---------------------------------------------------
 Sometimes sage can differentiate erf, but if there are two variables
 involved it gets confused in simplification and passes too many arguments
 to erf in maxima.

 {{{
 ----------------------------------------------------------------------
 | Sage Version 4.3.3, Release Date: 2010-02-21                       |
 | Type notebook() for the GUI, and license() for information.        |
 ----------------------------------------------------------------------
 sage: var('c x')
 (c, x)
 sage: diff(erf(x), x)
 D[0](erf)(x)
 sage: simplify(diff(erf(x), x))
 2*e^(-x^2)/sqrt(pi)
 sage: diff(erf(c * x), x)
 c*D[0](erf)(c*x)
 sage: simplify(diff(erf(c * x), x))
 ---------------------------------------------------------------------------
 TypeError                                 Traceback (most recent call
 last)

 /.../<ipython console> in <module>()

 /.../sage-4.3.3-linux-64bit-ubuntu_9.10-x86_64-Linux/local/lib/python2.6
 /site-packages/sage/calculus/functional.pyc
 in simplify(f)
      49     """
      50     try:
 ---> 51         return f.simplify()
      52     except AttributeError:
      53         return f

 /.../sage-4.3.3-linux-64bit-ubuntu_9.10-x86_64-Linux/local/lib/python2.6
 /site-packages/sage/symbolic/expression.so
 in sage.symbolic.expression.Expression.simplify
 (sage/symbolic/expression.cpp:21495)()

 /.../sage-4.3.3-linux-64bit-ubuntu_9.10-x86_64-Linux/local/lib/python2.6
 /site-packages/sage/symbolic/expression.so
 in sage.symbolic.expression.Expression._maxima_
 (sage/symbolic/expression.cpp:3435)()

 /.../sage-4.3.3-linux-64bit-ubuntu_9.10-x86_64-Linux/local/lib/python2.6
 /site-packages/sage/structure/sage_object.so
 in sage.structure.sage_object.SageObject._interface_
 (sage/structure/sage_object.c:3501)()

 /.../sage-4.3.3-linux-64bit-ubuntu_9.10-x86_64-Linux/local/lib/python2.6
 /site-packages/sage/interfaces/expect.pyc
 in __call__(self, x, name)
    1030
    1031         if isinstance(x, basestring):
 -> 1032             return cls(self, x, name=name)
    1033         try:
    1034             return self._coerce_from_special_method(x)

 /.../sage-4.3.3-linux-64bit-ubuntu_9.10-x86_64-Linux/local/lib/python2.6
 /site-packages/sage/interfaces/expect.pyc
 in __init__(self, parent, value, is_name, name)
    1449             except (TypeError, KeyboardInterrupt, RuntimeError,
 ValueError), x:
    1450                 self._session_number = -1
 -> 1451                 raise TypeError, x
    1452         self._session_number = parent._session_number
    1453

 TypeError: Error executing code in Maxima
 CODE:
         sage4 : (c)*(diff('erf(c, x), c, 1))$
 Maxima ERROR:

 Wrong number of arguments to erf
  -- an error. To debug this try: debugmode(true);
 }}}

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8568>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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