Re: Advanced expression simplification

On 2005-07-11, Igor Chudov <ichudov@algebra.com> wrote:
> 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.


If I look at your examples, a first order approach would be to
estimate the "terms" count of your initial expression, and pass that
count (or maybe +1 or +2) to the simplifying procedure telling it to
abort if more terms than that have been found.

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