Particular solve: find values of variables which will solve equation for any values of other variables

asked 2016-11-16 12:12:07 +0200

nib gravatar image

Hi, this is my first time using Sage, so I hope my questions aren't too trivial.

I have to solve the following problem: find (if they exist) values of real variables x,u,v (with x,v>0) such that the following equality

Maximum{2 a/x, 2 (ub + vc)/(u^2 + v^2), 2 ((u - x)(b - a) + vc)/(v^2 + (u - x)^2)} = (a/x + c/v) + (1/vx)sqrt( a^2 (u^2 + v^2) - 2 ax(bu + cv) + (b^2 + c^2)*x^2)

is verified for every value of the real values a, b, c. It is my understanding that to evaluate the maximum I should use max_symbolic, am I right?

Let me emphasize that I don't need to find values of x,u,v with respect to a,b,c, but fixed values of x,u,v which will verify the equality for any given a,b,c. This means that I need to find x, u, v which will verify all the infinite equations we will get for any different triple of values of a, b, c.

For this reason writing

x,u,v,a,b,c=var('x u v a b c') 

s1=solve([max_symbolic(2 a/x, 2*(u*b + v*c)/(u^2 + v^2), 2 ((u - x)*(b - a) + v*c)/(v^2 + (u - x)^2)) == (a/x + c/v)  +(1/v*x)*sqrt(a^2 (u^2 + v^2) - 2 a*x*(b*u + c*v) + (b^2 + c^2)*x^2)],x,u,v)


will not work. I've thought of solving for all 6 variables, but then an error occurred saying solve() could only use 5 positional arguments..

Can you suggest me any way to proceed? Also, I fear this kind of computation will be very heavy for my cpu.. Any ideas on how to make It lighter?

Thank you very much!

edit retag flag offensive close merge delete