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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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Mate

Posts: 389
Registered: 8/15/05
Re: can your CAS help proving inequalities?
Posted: Mar 9, 2013 8:33 AM
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On Mar 9, 2:07 pm, A N Niel <ann...@nym.alias.net.invalid> wrote:
> In article <khe8re$h5...@speranza.aioe.org>, Nasser M. Abbasi
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> <n...@12000.org> wrote:

> > On 3/8/2013 12:08 PM, cliclic...@freenet.de wrote:
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> > > Hello!
>
> > > Let a, b, c, d be arbitrary real numbers. Define:
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> > > r(a, b, c, d) := (a - c)*(a - d)*(b - c)*(b - d)
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> > > s(a, b, c, d) := (a + b)*(c + d) - 2*(a*b + c*d) - ABS((a - b)*(c - d))
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> > > t(a, b, c, d) := (a + b)*(c + d) - 2*(a*b + c*d) + ABS((a - b)*(c - d))
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> > > Can your CAS help proving the following inequalities?
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> > > MIN(r(a, b, c, d), r(a, c, b, d), r(a, d, c, b)) <= 0
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> > > MAX(s(a, b, c, d), s(a, c, b, d), s(a, d, c, b)) >= 0
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> > > MIN(t(a, b, c, d), t(a, c, b, d), t(a, d, c, b)) <= 0
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> > > Have fun!
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> > > Martin.
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> > Would showing that the CAS found {} as solution for
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> >     MIN(r(*)...) >0
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> > but found at least one solution for
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> >     MIN(r(*)...) <= 0
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> > qualify?
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> > --Nasser
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> In Maple, the response
> {}
> means there is no solution, while the response
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> (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.
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> What CAS did you use, and what does {} mean for it?


What about
solve({t*Zeta(1/2+I*t)=0, t>=0},t);
which returns
{t=0}







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