Comment #13 on issue 1620 by [email protected]: Allow derivatives of
unknown functions evaluated at a point
http://code.google.com/p/sympy/issues/detail?id=1620
Any implementation of this should respect issue 2070, that is,
Object.__class__(*Object.args) == Object, so the notation D[1,2](f)(x, y)
can only be used as syntactic sugar, not as a base for the implementation.
Ronan started to work on this in issue 1688, but it looks stalled. I think
this issue can be solved without 1688, although the approach there is more
elegant.
A simple way to do this is to have a class like:
DerivativeFunction(expr=f(x, y), variables=(x, y, 2), point=(1.5, z))
D(f(_x, _y), Tuple(_x, _y, _y), Tuple(1.5, z))
That way we can still use the handy diff(x,10) for specifying the order of
the derivative, and can also set the point of evaluation (that can default
to the differentiation variables if not given).
I'm not sure if it's better to write a new class to hold this or to extend
the current Derivative class. The latter leads to less code duplication but
requires change to all calls to Derivative in sympy, breaking
compatibility. The latter is easier to implement, but feels redundant,
because it's the same kind of object Derivative should represent.
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