
Re: can your CAS help proving inequalities?
Posted:
Mar 10, 2013 2:52 PM


On 3/10/2013 8:17 AM, Mate wrote:
> > There are many simple but tough inequalities, > e.g. the cyclic inequalities (Shapiro): > > x_1/(x_2+x_3) + x_2/(x_3+x_4) + ... + x_{n1}/(x_n + x_1) + x_n/(x_1 + > x_2) >= n/2 > > for x_i > 0. > > It would be interesting to know if Mathematica can manage these. > > So, what is Mathematica's answer for n in {6, 8, 10, 11, 14, 15}. > > (for n=14 there exists a counterexample, for n=15 the answer seems to > be not known). >
I am running it now for even n. But it is very time consuming, still waiting for n=6. For n=2, n=4 these are the results found so far:
{2, {{xx[1] > 1, xx[2] > 1}},
{4, {{xx[1] > 1, xx[2] > 1/2, xx[3] > 1, xx[4] > 1/4}}}}
{6, ..... will check in few hours ....}
Are these solutions listed somewhere? I searched but did not find them.
http://en.wikipedia.org/wiki/Shapiro_inequality
Nasser

