more Lisp code than LaTeX

My thesis is currently at about 35 pages.

I just realized that, despite this, I've written more Lisp code (~90k) than LaTeX code (~80k). Sure, it tooks about 8 times as long, but still. When I tell people that I write my philosophy in Lisp, I mean it as a joke... really.

challenge my equational reasoner!

I'm really proud of my equational reasoner. Challenge me!

Using the operations of +, -, *, /, ^, and the alphabet of numbers and variables, please come up with two very different finite expressions, which are equivalent under equational algebra. My claim is that my system will reduce them both to the same normal form, unless one (or both) of them is a polynomial division.

EXPRS := EXPR EXPRS
EXPRS := []
EXPR := (+ EXPRS)
EXPR := (* EXPRS)
EXPR := (^ EXPR EXPR)
EXPR := VAR
EXPR := NUMBER

(I have a vague suspicion that I'm reinventing Knuth-Bendix about 30 years too late).