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Long ago we did something similar in University studies (second year maybe) ... IIRC it was called minimal word (or term) problem.

In short you are transforming the term into a representation which allows a weighting function defining a maximum. The permutation (associativity, commutativity, ...) leading to the maximum is your normal form.

To terms leading to the same normal form are identical.

Sounds abstract but shouldn't be to difficult to achieve, e.g. normal forms of polynomials are easy, if you have different variables like in 5xy + 2xy *, give certain variables a (e.g. lexicographic) precedence (i.e. x>y) and order them by exponent.

If your terms are not transformable to polynomials it gets a bit more difficult...

Cheers Rolf

( addicted to the Perl Programming Language)

* ) which is a normal form of xy * (5x+2) * y


In reply to Re: List all different equations for a given one by LanX
in thread List all different equations for a given one by jess195

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