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Re: simplifying inequalities


On 17 Dec 2006, at 20:20, Chris Chiasson wrote:

> Why isn't the result of this command,
>
> FullSimplify[
>   beamLength>5 x&&2 beamLength>5 x&&3 beamLength>5 x&&
>     4 beamLength>5 x,{beamLength>x>0}]
>
> , equal to beamLength>5x?
>
> Mathematica just returns all the inequalities as input. Can something
> be done about this?
>
> --  
> http://chris.chiasson.name/
>

It seems that FullSimplify does not use CylindricalDecomposition in  
such cases:


CylindricalDecomposition[beamLength > 5*x && 2*beamLength > 5*x &&  
3*beamLength > 5*x && 4*beamLength > 5*x && beamLength > 0 && x > 0,
   {x, beamLength}]


x > 0 && beamLength > 5*x


Refine[%,x>0]

beamLength>5 x

CylindricalDecomposition is a function of very high complexity so  
FullSimplify and Simplify use it sparingly. I think Reduce always  
uses CylindricalDecompostion when inequalities are involved so it  
will also work in this case.

Andrzej Kozlowski


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