A N Niel
Posts:
2,255
Registered:
12/7/04


Re: can your CAS help proving inequalities?
Posted:
Mar 9, 2013 7:07 AM


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?

