Can I check if an inequality is true, and if not, get the conditions where the inequality could be true?

Question

Athulya Ram Sreedharan Nair 2020-6-25

0
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https://ww2.mathworks.cn/matlabcentral/answers/554317-can-i-check-if-an-inequality-is-true-and-if-not-get-the-conditions-where-the-inequality-could-be-t

回答： Vidhathri LNU 2020-6-30

Hello,

I am pretty new to Matlab. I have to check if an expression is positive, given some conditions. This is my code right now:

%general conditions
assume(0<beta & beta<alpha & alpha<1)
assumeAlso(b > 0 & p > 0 & c > 0 & f1 > 0 & f2 > 0 & f3 > 0 & f4 > 0)
%additional conditions
assumeAlso(f1 > f3)
assumeAlso(f1 > f3)
assumeAlso(alpha > 1/2)
assumeAlso(beta*f2 < f3)
assumeAlso(f4 < beta*(f1-f3))
isAlways((alpha*b*f3 + 2*b*beta*f1 - 2*b*beta*f3 - alpha*b*beta*f1 + alpha*b*beta*f3)/(alpha*f3 + beta*f1 - beta*f3) - (((b - 2*alpha*b)/alpha - alpha*(b/alpha + (f3 - beta*f2)/(alpha*beta)))/(alpha*f3 + beta*f1 - beta*f3) + (f4 - beta*f1 + beta*f3)/(alpha*f3 + beta*f1 - beta*f3))*(alpha*f3 + beta*f1 - beta*f3) > 0)

This is giving me a warning:

Warning: Unable to prove '0 < (alpha*b*f3 + 2*b*beta*f1 - 2*b*beta*f3 - alpha*b*beta*f1 +
alpha*b*beta*f3)/(alpha*f3 + beta*f1 - beta*f3) - (((b - 2*alpha*b)/alpha - alpha*(b/alpha + (f3 -
beta*f2)/(alpha*beta)))/(alpha*f3 + beta*f1 - beta*f3) + (f4 - beta*f1 + beta*f3)/(alpha*f3 + beta*f1 -
beta*f3))*(alpha*f3 + beta*f1 - beta*f3)'

Which I understand because there might be additional conditions which are needed for my expression to be positive.

Is there another method I can use instead of isAlways that can return me the conditions where this statement is true?