Comment #9 on issue 2476 by [email protected]: nth order Derivative
http://code.google.com/p/sympy/issues/detail?id=2476
So, moving on, I think changing internal representation of Derivative to
use args = (expr, (x, n1), (y, n2), ...) should work, as long as there's no
code that uses this representation directly (there's no way to maintain
compatibility of the internal variables). The old way of calling diff
should be accepted and converted, so that this works:
f(x, y, z).diff(x, x, (y, n), z, 2) == d^(3+n)/d^2x d^ny d^2z
_.args == (f(x, y, z), (x, 2), (y, n), (z, 2))
This should raise a ValueError if n is not integer.
To implement the expansion of arbitrary n-order derivative in the end of
comment 2, we need two things:
1. implement rules for composition and product: f(g(x)).diff((x, n)) and
(f(x)*g(x)).diff((x, n)).
2. implement a fdiffn() method for Functions or extend current fdiff() to
accept a 'difforder' parameter, that may be symbolic and defaults to 1 to
keep compatibility.
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