Comment #36 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
What should D(f) be?
What about a new class derived from Expr with .args = (Lambda of Function
object, *diffargs)? diffargs can be like current Derivative symbols (e.g.
(1, 1, 3, 2) that means d^4/dy dz dx^2 f(x, y, z)), or like the suggested
in issue 2476, a tuple of tuples, e.g. ((1, 2), (3, 1), (2, 1)) (same
meaning as before). Then D(f)(x) should return either the evaluated
expression, or an unevaluated Derivative (that may need Subs to be
expressed).
That way, the invariant from issue 2070 is satisfied, and we can add some
nice way to express higher order derivatives using slices, like D[1:2, 3,
2](f), which is the same object as above.
BTW, I'm assuming the numbering of function arguments to be the same as in
fdiff(), but I would be more satisfied with python numbering, starting with
0.
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