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Topic: can your CAS help proving inequalities?
Replies: 19   Last Post: Mar 11, 2013 12:00 PM

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A N Niel

Posts: 2,245
Registered: 12/7/04
Re: can your CAS help proving inequalities?
Posted: Mar 9, 2013 7:07 AM
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In article <khe8re$h58$1@speranza.aioe.org>, Nasser M. Abbasi
<nma@12000.org> wrote:

> On 3/8/2013 12:08 PM, clicliclic@freenet.de wrote:
> >
> > Hello!
> >
> > Let a, b, c, d be arbitrary real numbers. Define:
> >
> > r(a, b, c, d) := (a - c)*(a - d)*(b - c)*(b - d)
> >
> > s(a, b, c, d) := (a + b)*(c + d) - 2*(a*b + c*d) - ABS((a - b)*(c - d))
> >
> > t(a, b, c, d) := (a + b)*(c + d) - 2*(a*b + c*d) + ABS((a - b)*(c - d))
> >
> > Can your CAS help proving the following inequalities?
> >
> > MIN(r(a, b, c, d), r(a, c, b, d), r(a, d, c, b)) <= 0
> >
> > MAX(s(a, b, c, d), s(a, c, b, d), s(a, d, c, b)) >= 0
> >
> > MIN(t(a, b, c, d), t(a, c, b, d), t(a, d, c, b)) <= 0
> >
> > Have fun!
> >
> > Martin.
> >

>
> Would showing that the CAS found {} as solution for
>
> MIN(r(*)...) >0
>
> but found at least one solution for
>
> MIN(r(*)...) <= 0
>
> qualify?
>
> --Nasser
>


In Maple, the response
{}
means there is no solution, while the response

(that is, no response) means no solution was found. A third
possibility is where some solutions are shown, and then a disclaimer
that some solutions may have been lost.

What CAS did you use, and what does {} mean for it?



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