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Hi all,

http://lua-users.org/wiki/SymbolicDifferentiation

Ever since I had a brief affair with LISP in 1981, I've wanted to do
LISP-like things without typing so many damn parentheses. Well, as you
no doubt know, this kind of thing is quite natural to Lua.  This is
actually a spin-off from Penlight's func module, which constructs
expression trees to implement lambdas ('Placeholder Expressions').

Short summary: Differentiation is not hard, cleaning up afterwards
(simplification) can be challenging.  Also, using unbalanced
expression trees will drive you mad.

steve d.