
Re: can your CAS help proving inequalities?
Posted:
Mar 9, 2013 10:50 AM


Mate schrieb: > > 1. > Denoting > x:=r(a, b, c, d), y:=r(a, c, b, d), z:=r(a, d, c, b) > > ==> x*y+x*z+y*z = 0 > ==> min(x,y,z) <=0 and actually also max(x,y,z) >= 0 > > 2,3. > Denoting similarly x,y,z ==> > > y*z^3+2*y^2*z^2+y^3*z+x*z^3+4*z^2*y*x+4*z*y^2*x+y^3*x > +2*x^2*z^2+4*y*z*x^2+2*x^2*y^2+x^3*z+y*x^3 = 0 > ==> min(x,y,z) <= 0 and also max(x,y,z) >= 0 > > The relations in x,y,z can be easily verified with any CAS. > I have found them using Grobner bases in Maple. > > I had fun indeed. Thanks for the problems. >
Just noticed that the relation 2,3 can be factored into:
(x + y)*(x + z)*(y + z)*(x + y + z) = 0
Martin.

