Advanced expression simplification

I am writing an algebra expression simplifier. It parses an expression
and then applies various rules to the parsed tree. It also produces
"work shown". Much of it already works (reduction of constants,
similar terms, similar factors, etc). It works with expressions of
arbitrary complexity, powers etc.


                    http://www.algebra.com/services/rendering/simplifier.mpl


Now I am approaching more difficult areas.


Specifically, in simplification, some approaches can be tried and
abandoned. For example:


(x^2-1)/(x-1) simplifies to x+1. GOOD


(1^100-1)/(x-1) "simplifies" to x^99+x^98+...+x+1. NOT GOOD.




If I do such things, I need to make sure that simplification does not
loop with endless tries, and that it takes a reasonable amount of
time. Some approaches can initially lead to bigger expressions, and
then to smaller ones. The typical example is use of associative
property.


I cannot expect all simplification approaches to always reduce the
size of expressions. And yet, I need to know "where to stop".


Are there any good treatises on expression simplification.


thanks


i


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