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MathGroup Archive 2006

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Re: simplifying inequalities

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72286] Re: [mg72272] simplifying inequalities
  • From: "Chris Chiasson" <chris at chiasson.name>
  • Date: Mon, 18 Dec 2006 06:56:04 -0500 (EST)
  • References: <200612171120.GAA07329@smc.vnet.net>

Thank you Andrzej.

On 12/17/06, Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote:
>
> 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
>


-- 
http://chris.chiasson.name/


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