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Maxima does not solve the system sqrt(x)=1, y=1 with the solve function

I'm trying to solve system of equations with roots in maxima, for example:

solve([sqrt(x) = 1, y = 1], [x,y]);

But maxima says that this system has no solutions. On the other hand, maxima is able to solve this equation:

solve([sqrt(x) = 1], [x]);

Can I solve systems like the above in maxima?

Solution

  • The built-in solve has serious limitations. The add-on function to_poly_solve can solve equations which contain radicals; I don't know what its limitations are.

    (%i2) load (to_poly_solve);
(%o2) /usr/local/share/maxima/5.40.0/share/to_poly_solve/to_poly_solve.mac
(%i3) to_poly_solve ([sqrt(x) = 1, y = 1], [x,y]);
(%o3)                       %union([x = 1, y = 1])

    %union means a union of solutions. Since there is only one solution found, %union could be simplified away; its presence is perhaps a little inconvenient, but not incorrect.