Re: Hyperbolic function identity

• To: mathgroup at smc.vnet.net
• Subject: [mg51025] Re: Hyperbolic function identity
• From: carlos at colorado.edu (Carlos Felippa)
• Date: Sat, 2 Oct 2004 03:17:51 -0400 (EDT)
• References: <200409300852.EAA26465@smc.vnet.net> <EC6856EA-12D4-11D9-8846-000A95B4967A@mimuw.edu.pl> <E5587780-12E6-11D9-9AC3-000A95B4967A@mimuw.edu.pl> <415C2570.8050607@wolfram.com> <cjj840\$bsd\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote in message news:<cjj840\$bsd\$1 at smc.vnet.net>...
> 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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