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Can someone help me understand the scalar product of problem 23 in the attached practice sheet? I should show that this defines a nondegenerated symmetric scalar product on the vector space of trivariate polynomials. My problem is that I don't understand the argument of $P$. An example would be great!

Thank you.

The sheet is in german, but all you need to know is above :)

Practice Sheet

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up vote 2 down vote accepted

This is just a notation/formal calculation. Just plug in the differential operators into the polynomial $P$ and apply the resulting operator to $Q$ and evaluate at $(0,0,0)$.

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Thank you, do you have any hints how i can write that down formally? and $(d/dx)^2$ for example is the second derivative right? – PaulH Oct 30 '13 at 0:58

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