Hi all:

Pardon my re-post of this message.  I forgot to update the subject
line.

Thanks to those who worked on closing ticket 6243 regarding
derivatives as dictionary keys for the release of Sage 4.1.1.  It
appears that there's still a bug, though (see below).

Alex

----------------------------------------------------------------------
| Sage Version 4.1.1, Release Date: 2009-08-14
|
| Type notebook() for the GUI, and license() for information.
|
----------------------------------------------------------------------
sage: f= function('f',x)
sage: d= {}
sage: for i in [1..5]:
....:     print diff(f,x,i)
....:     d[diff(f,x,i)] = i
....:
D[0](f)(x)
D[0, 0](f)(x)
---------------------------------------------------------------------------
NotImplementedError                       Traceback (most recent call
last)
/Users/arai021/<ipython console> in <module>()
/Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
expression.so in sage.symbolic.expression.Expression.__nonzero__
(sage/
symbolic/expression.cpp:7659)()
/Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
expression.so in sage.symbolic.expression.Expression.test_relation
(sage/symbolic/expression.cpp:9032)()
/Applications/sage/local/lib/python2.6/site-packages/sage/rings/
complex_interval_field.pyc in __call__(self, x, im)
    286
    287             try:
--> 288                 return x._complex_mpfi_( self )
    289             except AttributeError:
    290                 pass
/Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
expression.so in sage.symbolic.expression.Expression._complex_mpfi_
(sage/symbolic/expression.cpp:5329)()
/Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
expression_conversions.pyc in __call__(self, ex)
    212                 div = self.get_fake_div(ex)
    213                 return self.arithmetic(div, div.operator())
--> 214             return self.arithmetic(ex, operator)
    215         elif operator in relation_operators:
    216             return self.relation(ex, operator)
/Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
expression_conversions.pyc in arithmetic(self, ex, operator)
   1424             return base ** expt
   1425         else:
-> 1426             return reduce(operator, map(self, operands))
   1427
   1428     def composition(self, ex, operator):
/Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
expression_conversions.pyc in __call__(self, ex)
    216             return self.relation(ex, operator)
    217         elif isinstance(operator, FDerivativeOperator):
--> 218             return self.derivative(ex, operator)
    219         else:
    220             return self.composition(ex, operator)
/Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
expression_conversions.pyc in derivative(self, ex, operator)
    344             NotImplementedError: derivative
    345         """
--> 346         raise NotImplementedError, "derivative"
    347
    348     def arithmetic(self, ex, operator):
NotImplementedError: derivative

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