I am trying to solve an equation with Maxima so that I only get real solutions if they exist; if there are no real solutions, or if there are not even complex solutions, I would like Maxima to return an empty list.
For example, I would like that when solving x^2+100-x=0 using solve(x^2+100-x,x), which has only complex solutions, Maxima would return an empty list. Or that when solving log(x)-x=0 using solve(log(x)-x,x), which also has no real solutions, Maxima would return an empty list. In this second example, what I get instead is [x=log(x)].
How could this be achieved with Maxima?
Inhibit implicit solutions:
(%i1) solve(log(x)-x);
(%o1) [x = log(x)]
(%i2) solve(log(x)-x), solveexplicit: true;
(%o2) []
Keep only solutions without an imaginary part:
(%i1) s: solve(x^2+100-x);
sqrt(399) %i - 1 sqrt(399) %i + 1
(%o1) [x = - ----------------, x = ----------------]
2 2
(%i2) sublist(s, imagpart);
(%o2) []
(%i3) s: solve(x^2+2 * x + 1);
(%o3) [x = - 1]
(%i4) sublist(s, imagpart);
(%o4) [x = - 1]