3 equation system causes 3 different crashes

[Brian Zilli]

I recently came across this YouTube video on the 50g’s solving ability, and decided to try these problems out on the Prime G2.

The last system of equations in the video was the most interesting, since it presents three different ways to cause the Prime to crash.

WARNING: Make sure to back up your Prime before trying any of these. The first two just cause a “Rebooting” message, which I presume doesn’t affect memory other than restoring to a previous RAM state; but the last one causes the screen to fill with random noise before a reboot, so I don’t know how that affects file integrity.

Method 1: The Solver App

If you enter the system Z^3=Y^2*X, sqrt(X) = LOG(3*Z^2), 5*Z*X=Y^X in the solver app and use the initial guess from the video (Z=Y=X=1), the solver converges on a solution just fine.

Given the default initial guess of Z=X=Y=0, the calculator correctly throws an error saying that it could not find a solution.

But if you start with the initial guess Z=0, Y=0.5, and X=0, it will force a reboot and RAM restore.

Method 2: CAS Numerical Solve

fsolve([z^3=y^2*x, sqrt(x)=log10(3*z^2), 5*z*x=y^x], [x, y, z]) (without an initial guess) causes a reboot and RAM restore. Like in the Solve app, the same does not happen with the initial guess [1, 1, 1], but it does happen with [0, 0.5, 0].

The reboot also happens with [0, 0, 0] as a guess, so I assume the CAS’s numerical solver is different from that used by the Solve app.

Method 3: CAS Symbolic Solve

solve([z^3=y^2*x, sqrt(x)=log10(3*z^2), 5*z*x=y^x], [x, y, z])

The hourglass spins for a short while, then the screen fills with random junk and the system reboots. My naive assumption is that this is a memory overflow into the frame buffer, but I really have no idea.

Finally, a disclaimer: The initial guesses of [0, 0, 0] and [0, 0.5, 0] are clearly "bad" in the sense that they are outside of the domain of the second equation, which gives the numerical solver nothing to work with. One should also not expect a symbolic solution to exist for such a system. I understand this. But, given that the Prime's target audience is students, many of them will not understand this, so (in their exploration of the Prime and mathematics in general) they may try something like this.