Anything simple always interests me.
Chapter 8 started with high hopes: to take an existing pattern matcher, copy down some mathematical identities out of a reference book, and come up with a usable symbolic algebra system. The resulting system was usable for some purposes, and it showed that the technique of rule-based translation is a powerful one. However, the problems of section 8.5 show that not everything can be done easily and efficiently within the rule-based pattern matching framework.
There are important mathematical transformations that are difficult to express in the rule-based approach. For example, dividing two polynomials to obtain a quotient and remainder is a task ...