> Do you need each combination once

Yes.  I think that's correct, my bad.  See wiki (I think, that the Courant&Hilbert [example](http://en.wikipedia.org/wiki/Euler%E2%80%93Lagrange_equation#Single_function_of_two_variables_with_higher_derivatives) was right, but wiki's reference to the Einstein summation convention was wrong).

> can you add such a test?

ok, done.