Hello,

On Sun, Jun 19, 2011 at 3:51 PM, Mani Chandra <[email protected]> wrote:
> Hi,
> Is it possible to tell simplify that the partial derivatives with respect to
> two different variable commute so that it can simplify further? For ex:
> d^2 f/dxdy + d^2 f/dydx
> The above expression is left as it is by simplify(), but it would be nice if
> there were some way to tell it about the commutation so that it can simplify
> further.

This is fixed in current development version, so that

>>> f(x, y).diff(x, y) - f(x, y).diff(y, x)
0

If you don't want this to happen, you have to use unevaluated
derivatives (diff() always evaluates them):

>>> Derivative(f(x, y), x, y) - Derivative(f(x, y), y, x)
D(f(x, y), x, y) - D(f(x, y), y, x)

Cheers,
Renato

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