Algebraic Simplification: A Guide for the Perplexed Algebraic simplification is examined first from the point of view of a user who needs to comprehend a large expression, and second from the point of view of a designer who wants to construct a useful and efficient system. First we describe various techniques akin to substitution. These techniques can be used to decrease thesize of an expression and make it more intelligible to a user. Then we delineate the spectrum of approaches to the design of automatic simplification capabilities in an algebraic manipulation system. Systems are divided into five types. Each type provides different facilities for the manipulation and simplification of expressions. Finally we discuss some of the theoretical results related to algebraic simplification. We describe several positive results about the existence of powerful simplification algorithms and the number-theoretic conjectures on which they rely. Results about the nonexistence of algorithms for certain classes of expressions are included. CACM August, 1971 Moses, J. algebraic manipulation, algebraic simplification, canonical simplification 3.1 3.2 3.6 4.9 5.2 5.9 CA710805 JB February 2, 1978 3:42 PM 1396 4 2167 1396 4 2167 1946 4 2167 2167 4 2167 2167 4 2167 2167 4 2167 2167 4 2167 2857 4 2167 2956 4 2167 1379 5 2167 1393 5 2167 1392 5 2167 2167 5 2167 2167 5 2167 2167 5 2167 2164 5 2167 2169 5 2167 2170 5 2167 2323 5 2167 2719 5 2167 1626 6 2167 210 6 2167 2151 6 2167 2164 6 2167 2165 6 2167 2167 6 2167 2167 6 2167 2167 6 2167 2167 6 2167 2166 6 2167 2170 6 2167 2210 6 2167 2645 6 2167 2657 6 2167