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Re: Hyperbolic function identity

Andrzej Kozlowski <akoz at> wrote in message news:<cjj840$bsd$1 at>...
> Ah, of course! Well, it was late last night!
> Still, I think this explains the whole problem, and also shows that  
> with the present paradigm on which Simplify and FullSimplify are based 
> it is unavoidable.
> To summarise it: with a given complexity function and the presence of 
> conditions in Simplify or FullFimplify, the transformation leading to 
> the "simplest result' (in this case 0) may have to use a step which 
> results in an expression which has a higher complexity (in this case 
> the expression involving logs, which has a higher default complexity 
> until it itself is simplified under the given assumptions). Clearly, 
> this is un-avoidable, since to avoid it Mathematica should test each 
> intermediate expression that any of its trasformation functions 
> produces by again applying FullSimplify with assumptions. IN other 
> words it would would have to do something like this:
Can this long discussion be summarized as follows:

   The paradigm of using a leaf-based complexity function as
   simplification driver is wrong.

I happen to be interested in the subject because more of 80% of the
problems I have experienced with Mathematica since 1994 are due to
Simplify, and more recently FullSimplify.  The main difficulties are

 o   Excessive time requiring user abort 
     Note 1: specifying a TimeConstraint, which appeared in 3.1,  
             does not work as regards limiting total time
     Note 2: my feeling is that  the tree-traversal algorithm used 
             has exponential complexity  in the number of leaves,  
             but I have no timing tests to back that estimate.

 o   Outside coaching to tunnel out from local minima.  Simplify 
       should be a black box.   Tunneling algorithms are well 
       known in the MP community.

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