An Algebraic Simplify Program in LISP. AIM-011

A program which performs 'obvious' (non-controversial) simplifying
transformations on algebraic expressions (written in LISP prefix
notation) is described. Cancellation of inverses and consolidation
of sums and products are the basic accomplishments of the program;
however, if the user desires to do so, he may request the program to
perform special tasks, such as collect common factors from the
products in sums or expand products. Polynomials are handled by
routines which take advantage of the special form by polynomials; in
particular, division (not cancellation) is always done in terms of
polynomials. The program (run on the IBM 7090) is slightly faster
than a human; however, the computer does not need to check its work
by repeating the simplification.

Although the program is usable -- no bugs are known to exist -- it
is by no means a finished project. A rewriting of the simplify
system is anticipated; this will eliminate much of the existing
redundancy and other inefficiency, as well as implement an
identity-recognizing scheme.