Re: simplifying inequalities

*To*: mathgroup at smc.vnet.net*Subject*: [mg72280] Re: [mg72272] simplifying inequalities*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Mon, 18 Dec 2006 06:55:42 -0500 (EST)*References*: <200612171120.GAA07329@smc.vnet.net>

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

**References**:**simplifying inequalities***From:*"Chris Chiasson" <chris@chiasson.name>