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MathGroup Archive 2011

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Re: Inequality


On 10 Oct 2011, at 10:25, ff mm wrote:

>
> Thank a lot
> If I can use functions to judge the inequality ture directly
>
>
>
>

I assume that by "directly" you mean something like 
Assuming[assumptions,FullSimplify[inequalities]] returning True. This is 
what works in many simpler cases but not in the one you posted. At this 
time this is too hard a problem for FullSimplify or any other function 
in Mathematica (and I suspect other similar programs). Firstly, the 
problem has to be reduced to one involving analytic functions of one 
variable and this needs a small mathematical trick which I don't think a 
computer program is likely to attempt without human help (though it 
might be possible to implement this sort of heuristics). Secondly, the 
ability to solve such inequalities depends on mathematical techniques  
that are only used by Reduce (and, in version 8, by Solve) but not by 
FullSimplify. I believe that the reason for this is that Reduce and 
Solve are "solvers" and FullSimplify are simplifiers, and while their 
areas of applicability overlap they do not coincide. In particular, 
FullSimplify works by trying to reduce an expression to a "simpler form" 
"step by step" but the methods needed to solve problems do not fit into 
this sort of pattern.

Of course, it is quite possible that in the future FullSimplify will be 
able to solve this problem and many others "directly" - but I am sure 
there will always remain problems of this and other kinds that will 
first require intelligent human intervention before Mathematica can be 
usefully applied to them.

Andrzej



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