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.

This memo gives empirical justification for the assumption that the

number of bisections of an NxN (N even) checkerboard is

approximately given by the binomial coefficient (A, A/2) where 2A is

the length of the average bisecting cut.