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MathGroup Archive 2006

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Re: Re: unable to FullSimplify


On 20 Apr 2006, at 18:14, Vladimir wrote:

> Andrzej Kozlowski wrote:
>> Well, it seems to me that you are expecting too much.
>
> Well, yes, considering the internal simplification and
> related code is supposedly thousands of pages long.
>
>> x + x^4 + 4*x^5 + 6*x^6 + 4*x^7 + x^8
>>
>> there are just too many different groupings and rearrangements that
>> would have to be tried to get to a simpler form.
>
> According to documentation, "FullSimplify effectively has to try
> combining every part of an expression with every other".

Yes, you are right. I wrote that without giving it much thought; my  
only really significant point was the one about the need to use only  
complexity decreasing transformations and this still stands.
>
>> Sometimes the only
>> way to transform an expression to a simpler form is by first
>> transforming it to a more complex one
>
> I'm sure FullSimplify can be improved without the need
> for such complexification steps. For example:
>
> In[]:= subdivide[a_ + b_] := FullSimplify[a] + FullSimplify[b];
>          FullSimplify[Expand[x + (x + x^2)^4],
>            TransformationFunctions -> {Automatic, subdivide}]
>
> Out[]= x + x^4*(1 + x)^4
>

Well, yes, it works nicely here but the question is, if you make this  
a default transformation transformation for FullSimplify how will it  
effect complexity? If you have a sum of n terms you will have to  
break it up into all possible pairs, then apply FullSimplify to each,  
and then keep doing this recursively. In fact it even seems hard to  
see how you would avoid numerous unnecessary attempts at simplifying  
the same expression... Obviously complexity is a very important  
consideration i choosing default functions for FullSimplify.  
Functions like subdivide should be added by users when they see the  
need for it.

Andrzej Kozlowski


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