The function mixpar will take nested calls to diff, and sort the sequence of differentiations so that they are sorted by lexicographical ordering on the variables of differentiation.

The purpose of this function is to ensure that equal mixed partials are recognized as equal.

The command with(difforms,mixpar) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{difforms}\right)\:$$\mathrm{defform}\left(f=0\,x=0\,y=0\,z=0\right)$

$d\left(f\left(x\,y\,z\right)\right)$

$\left(\frac{\partial }{\partial x}f\left(x\,y\,z\right)\right)d\left(x\right)+\left(\frac{\partial }{\partial y}f\left(x\,y\,z\right)\right)d\left(y\right)+\left(\frac{\partial }{\partial z}f\left(x\,y\,z\right)\right)d\left(z\right)$

$d\left(\right)$

$0$

$\mathrm{mixpar}\left(\right)$

$\mathrm{mixpar}\left(0\right)$