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MathGroup Archive 2006

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Re: Re: Re: Simplifying in Mathematica


On 11 Nov 2006, at 17:39, Daniel Lichtblau wrote:

> pierodancona at gmail.com wrote:
>> Define a function (depending on the variables B,b,A,a,c,d...etc,
>> all of them) equal to your expression, and compute it at many points.
>> If the expression is 0, the result should always be 0. Notice that if
>> your expression is a polynomial or rational and you choose your
>> points in a "not too special" way, this gives actually a rigorous
>> "proof"
>> that the expression is 0. In general, this is an extrremely reliable
>> heuristic (and of course a "proof" if you do not get 0 for some
>> values).
>>
>> I encounter the same problem frequently, and this method works
>> very well, also to test if two complicated expressions are the same
>> or not (guess how :)
>>
>> Piero
>>
>>
>>
>> 330006 at gmail.com wrote:
>>
>>> I have a function which is a sum of many terms which look like this:
>>>
>>> (2*(B-b)^2 - 2*(A-a)*c*d^2)/(4*b^2*(1-c*2)*d^2)
>>>
>>> I think the function is actually equal to 0, but I have a hard  
>>> time in
>>> trying to simplify it in Mathematica. Any ideas or commands I should
>>> try? Any suggestions in general about simplifying formulas will also
>>> be greatly appreciated!
>>>
>>> Thanks a lot!
>
>
> Random point evaluation, and various other heuristics, are what lie
> behind the Mathematica predicate Developer`ZeroQ.
>
>
> Daniel Lichtblau
> Wolfram Research
>

Another possible approach is to evaluate NMaximize[Abs[expr],vars],  
where expr is the expression suspected of being zero and vars the  
variables.

Andrzej Kozlowski


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