Solve takes forever without error message for certain input values

Hello, I try to solve following equation using matlab (R2016a+Symbolic Toolbox):

syms R2

eta=(2*R2 + 499999999999999999999999974/5)/(2*(99999999999999999999999999*R2 - 1549999999999999999999999987/5)) - 28670157817202169/38280596832649216

u =- (500000000000000000000000000*R2)/(31*(99999999999999999999999999*R2 - 1549999999999999999999999987/5)) - 3511406642924695/36028797018963968

v =3511406642924695/36028797018963968 - (500000000000000000000000000*R2)/(31*(99999999999999999999999999*R2 - 1549999999999999999999999987/5))

R2a=solve(eta==sqrt(abs(u*v)),R2);
R2a=double(R2a)
R2b=solve(eta==-sqrt(abs(u*v)),R2);
R2b=double(R2b)
R2ges=transpose([transpose(R2a) transpose(R2b)])

This works fine and will deliver two solutions for R2 in seconds. However the same code with different input parameters eta u and v will not give a solution in reasonable time without bringing any kind of error message.

syms R2

eta =(2*R2 + 4499999999999999999999999801/45)/(2*(99999999999999999999999999*R2 - 2711111111111111111111111089/10)) - 4465535319756041/38280596832649216

u =- (1125000000000000000000000000*R2)/(61*(99999999999999999999999999*R2 - 2711111111111111111111111089/10)) - 7022813285849393/72057594037927936

v =7022813285849393/72057594037927936 - (1125000000000000000000000000*R2)/(61*(99999999999999999999999999*R2 - 2711111111111111111111111089/10))

R2a=solve(eta==sqrt(abs(u*v)),R2);
R2a=double(R2a)
R2b=solve(eta==-sqrt(abs(u*v)),R2);
R2b=double(R2b)
R2ges=transpose([transpose(R2a) transpose(R2b)])

If I stop the code, I get the following message:

Operation terminated by user during mupadengine/evalin (line 102)

    In mupadengine/feval (line 158)
                [S,err] = evalin(engine,stmt,'message');

    In solve (line 292)
    sol = eng.feval('solve', eqns, vars, solveOptions);

    In forum_test (line 29)
    R2a=solve(eta==sqrt(abs(u*v)),R2);

Do you have any ideas how to resolve the problem? I want to solve this equation a lot of times in order to find certain cases that fulfill other conditions. However, if in a loop iteration, one of the "solve" lines takes forever, this does obviously not work and will make it very impractical for example to have a lot of iterations run over night.

Thanks and best regards, Tina

[Torsten]

What you have after multiplication with the denominators is a polynomial equation of 4th degree in R2. There is an analytic solution formula for such polynomials. Why don't you use it directly ?

Best wishes

Torsten.

[Tina Gottwald]

Hello, I did not use a direct analytical solution for a polynomial because the "type" of polynomial you get can vary depending on other input parameters (the code shown here is a very small part of a more complex calculation). It may be difficult to code all the possible cases with an "own" analytical formula.

I know that there will not always be a real solution for R2. If there is none, then the code should simply continue with the next iteration. I just tried to use the Return Parameters to keep the code from taking forever to try to find a solution, but so far without much success. It takes about 15 Minutes before the code continues in some cases... I

Answer 1

[Tina Gottwald]

The problem could be solved the following way:

syms R2

assume (R2, 'real') 
eta =(2*R2 + 4499999999999999999999999906/45)/(2*(99999999999999999999999999*R2 - 772222222222222222222222217/5)) + 37229654178979847/76561193665298432

u =7022813285849389/72057594037927936 - (4500000000000000000000000000*R2)/(139*(99999999999999999999999999*R2 - 772222222222222222222222217/5))

v =- (4500000000000000000000000000*R2)/(139*(99999999999999999999999999*R2 - 772222222222222222222222217/5)) - 7022813285849389/72057594037927936

[R2a]=solve(eta==sqrt(abs(u*v)),R2)
R2a=double(R2a)
 R2b=solve(eta==-sqrt(abs(u*v)),R2);
 R2b=double(R2b)
 R2ges=transpose([transpose(R2a) transpose(R2b)])

The line assume( R2, 'real') did the trick for me as I'm only looking for real solutions. The code is now fast and runs without problems.