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/

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