I'd like to know how to ask Maple to find numerical solutions to underspecified systems of nonlinear equations. For example, suppose I had a system of equations like this:
eq1 := y1 = tanh(x1);
eq2 := y2 = cosh(x1 + x2);
eq3 := y1 + y2 = 2.0;
Typing this:
fsolve([eq1, eq2, eq3]);
results in the following error:
Error, (in fsolve) number of equations, 3, does not match number of variables, 4
In this situation I can easily artificially restrict the system to find a solution. For example, I can do:
eq4 := x1 = 0.0;
fsolve([eq1, eq2, eq3, eq4]);
which will result in the following solution:
{x1 = 0., x2 = 1.316957897, y1 = 0., y2 = 2.000000000}
The issue here is that I pulled x1 = 0.0; out of thin air. Setting a single variable to zero would not work to solve an arbitrary set of nonlinear equations. How can I ask Maple to find a single (not necessarily unique) solution to an underspecified system of nonlinear equations?
