Comment #36 on issue 1816 by [email protected]: Adding partial
derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
I think we can all agree that in Lagrangian mechanics, we take the partial
derivatives of L w.r.t it's first, second, and third arguments (say q, r,
and t, as in Comment 32) and evaluate the derivatives at the point (q=x(t),
r=x'(t), t=t), also as in Comment 32.
As Brian mentions, he has implemented in his branch the substitution steps
that were performed manually in Comment 32. I find this functionality very
useful and think it would be great if .diff() could do those substitution
steps for me.
In regards to taking derivatives wrt named functions, I agree this is a
little odd and probably not particularly useful, but still valid.
Mathematica does it too:
http://www.wolframalpha.com/input/?i=D%5BCos%5Bx%5D*Cos%5Bx%5D%2C+Cos%5Bx%5D%5D
So what are the holdups for accepting this? I'm not clear what they are,
but if there are any, it would be great to see an example piece of code
that uses Brian's implementation and gives an incorrect or ambiguous result.
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