OK, I got some results, although I'm not sure if they're correct: all of
the 2nd order partial derivatives are zero or very close to zero. (Same
with the 1st order partials, but that's plausibly OK -- e.g. we are
looking at a local minimum of some function. Just guessing of course.)
I reorganized the computations to construct a formal Taylor series and
work on that before substituting in the actual definitions. Note that
some of the intermediate results are still very large -- circa 50,000
terms. Dunno if that's to be expected or strange. It may well be that
there is still another, better way to go about it.
Released versions of Maxima cannot run the attached script -- there is a
bug in PARTITION which is tickled by expressions containing dummy
variables ("at" in this case). I fixed the bug, patch attached for reference
(I pushed the commit already). You'll have to recompile in order to run
the script. Or take a different approach which doesn't trigger the bug.
Well, I don't know if I've accomplished anything but anyway here it is.
It was, as they say, a learning experience.
best
Robert Dodier
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