
Re: can your CAS help proving inequalities?
Posted:
Mar 9, 2013 1:04 PM


On 3/9/2013 6:07 AM, A N Niel wrote:
> > 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? >
Mathematica. It has a special command called
"FindInstance[expr, vars]
finds an instance of vars that makes the statement expr be True. gives results in the same form as Solve: if an instance exists, and {} if it does not. "
http://reference.wolfram.com/mathematica/ref/FindInstance.html
So that is what I used:
 Remove["Global`*"] 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)] 
and now
 FindInstance[ Min[r[a, b, c, d], r[a, c, b, d], r[a, d, c, b]] > 0, {a, b, c, d}]
{}
FindInstance[ Min[r[a, b, c, d], r[a, c, b, d], r[a, d, c, b]] > 0, {a, b, c, d}]
{}
FindInstance[ Min[t[a, b, c, d], t[a, c, b, d], t[a, d, c, b]] > 0, {a, b, c, d}]
{} 
But I was not sure this qualifies as "proof" that is why I asked first.
Nasser

