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MathGroup Archive 2006

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Re: Inequalities

  • To: mathgroup at smc.vnet.net
  • Subject: [mg69778] Re: Inequalities
  • From: dimmechan at yahoo.com
  • Date: Sat, 23 Sep 2006 04:43:54 -0400 (EDT)
  • References: <eeqpop$oe3$1@smc.vnet.net><eetu1g$8t7$1@smc.vnet.net>

Actually in my posts I have a mistake :

<< "Algebra`InequalitySolve`"

InequalitySolve[p*(1 - p) < q*(1 - q) && 0 < p < q < 1, {p, q}]
0 < p < 1/2 && p < q < 1 - p

Reduce[p*(1 - p) < q*(1 - q) && 0 < p < q < 1, {p, q}]
0 < p < 1/2 && p < q < 1 - p

Now the two outputs are the same.


Î?/Î? dimmechan at yahoo.com έγÏ?αÏ?ε:
> I repost this message with corrections
>
> Hi.
>
> You can use Reduce
> (http://documents.wolfram.com/mathematica/functions/Reduce)
>
> Reduce[p*(1 - p) < q*(1 - q) && 0 < p < q < 1, {p, q}]
> 0 < p < 1/2 && p < q < 1 - p
>
> There is also the package InequalitySolve
> (http://documents.wolfram.com/v5/Add-onsLinks/StandardPackages/Algebra/InequalitySolve.html)
>
> <<Algebra`InequalitySolve`
>
> InequalitySolve[p*(1 - p) - q*(1 - q) > 0 && 0 < p < q < 1, {p, q}]
> (Inequality[0, Less, p, LessEqual, 1/2] && 1 - p < q < 1) || (1/2 < p <
> 1 && p < q < 1)
>
> Dimitris Anagnostou
>
>
> Î?/Î? misha έγÏ?αÏ?ε:
> > I am an inexperienced user and am wondering whether Mathematica can help
> > me with inequalities such as the following.
> >
> > Given 0 < p < q < 1,
> >
> > When is p(1-p)<q(1-q)?
> > 
> > It should be, if 1 - q > p.
> > 
> > Thanks!


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