A few months ago, when I was very new to Maxima, I posted my solutions to several multivariable optimization problems, and included a standard constrained optimization example for which the built in command solve failed.
Here’s the problem:
In my multivariable calculus class, we’ve just encountered that problem again. What my students and I discovered was that the order of the variables as specified by the user in the argument list caused the command to either succeed or fail, as you can see from the first two lines below:
I wrote to the experts at email@example.com. They replied en masse very quickly and were very generous with their time and advice. They verified the problem, pointing out that solving systems of equations is really complicated, and that the solve program seeks to solve for the variables one at a time and things can go wrong if an inauspicious order of variables is followed.
The experts also tried our problem with the package to_poly_solve, and happily it succeeded without the hassle of needing to specify the variables in the right order. For solve users who reference the solutions it produces as elements of a list, direct use of to_poly_solve presents a challenge due to output in a format different from that of solve — t0_poly_solve returns solutions as a set with %union.
I’ve written a little wrapper Ksolve.mac that is called like solve as illustrated above.
In Ksolve if an initial call to solve fails, the process automatically upgrades to to_poly_solve in several variations, and (hopefully) returns solutions in the same format as solve.