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Motivation: I need to take higher derivatives with respect to many variables. The particular derivatives I take are based on a homogeneous multivariate polynomial. This polynomial is 12 pages in Maple for a 16-dimensional algebra thus we need to find a way to construct the derivative operator automatically.

I think if someone can explain how to solve the problem below then we can extrapolate for the ugly cases in which the technique is required:

Question: given $P = xyz+x^2y+xz^2+z^3$ what Maple code will allow me to convert $P$ to the differential expression $Du = u_{xyz}+u_{xxy}+u_{xzz}+u_{zzz}$?

The best answer is easily generalized to other $4^{th}$,$5^{th}$ etc... order multinomials.

Thanks in advance for any advice!

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up vote 1 down vote accepted

There is a great command in the PolynomialTools package.woo hoo, it works!

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