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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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clicliclic@freenet.de

Posts: 982
Registered: 4/26/08
Re: can your CAS help proving inequalities?
Posted: Mar 9, 2013 10:50 AM
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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.



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