Comment #44 on issue 1816 by hazelnu...@gmail.com: Adding partial
derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
Aaron:
expr.subs(function, Dummy('x')).diff(Dummy('x')).subs(Dummy('x'),
function)
Makes perfect sense to me and I think is very useful. In contrast to
Ronan's stance in Comment 43, I *don't* want to have to explicitly
substitute-transform-backsubstitute every time, and I think many people who
are doing variational calculus would feel the same.
The reason is that if you consider an expression to be a function of some
Function
in the expression, say F(f(x)), then F(u) means exactly the same thing as
expr.subs(f(x), u) in SymPy.
begs the question of whether a Functional class should be created. This is
bound to be a huge can of worms and I don't think it should block Brian's
request, but is probably worth thinking about.
I am fine with Brian's implementation as long as there is a statement in
the docstring that explicitly states that we are simply substituting
non-Symbol instances with dummy Symbols, differentiating wrt to those
symbols, and back-substituting non-Symbol instances. From what I can tell,
Brian has stated this in the docstrings for Derivative, Expr, and his
comments throughout the code clearly state what he is doing.
Ronan: Am I correct in understanding that you don't find the following
functionality to be something that should be automatically handled by
diff():
t = Symbol('t')
xfunc = Function('x')
x = xfunc(t)
diff(2 * x + 4, x)
2
Instead, would you prefer *users* to enter:
_x = Dummy('x')
(2 * x + 4).subs(x, _x).diff(_x).subs(_x, x)
Also, you mention "I'm quite sure that it has many puzzling and
mathematically inconsistent consequences." Could you give us some examples?
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