Solving symbolic equation in matlab

Question

I am trying to solve a symbolic equation of the form

D = lamda^12/339288145381785600000 + lamda^10/18124366740480000 +
    lamda^8/7846046208000 + lamda^6/523908000 + lamda^4/25200

where lamda is declared as sym . The output I get is not in a readable form. Even vpa is not giving me the answer in readable form. what can be the solution?

Answer 1

First we define the symbolic function:

syms x
f(x) = x^12/339288145381785600000 + x^10/18124366740480000 + ...
    x^8/7846046208000 + x^6/523908000 + x^4/25200;
ezplot(f)

Next we find the roots (by solving it numerically). You could also use the vpasolve MATLAB function:

sol = feval(symengine, 'numeric::solve', f==0, x)

There is 1 real solution and 8 complex ones:

>> sol(:)
sol =
   79.624598247213536847657202795915 - 49.037140566365604310129811798328*i
   79.624598247213536847657202795915 + 49.037140566365604310129811798328*i
                                       118.88396448746822093664197370373*i
                                      -118.88396448746822093664197370373*i
                                      -111.61305465738189638915837157361*i
                                       111.61305465738189638915837157361*i
                                                                         0
 - 79.624598247213536847657202795915 - 49.037140566365604310129811798328*i
 - 79.624598247213536847657202795915 + 49.037140566365604310129811798328*i

Finally we plot the roots:

s = double(sol);
plot(real(s), imag(s), 'r.', 'MarkerSize',25)
axis square; axis([-100 100 -150 150]); box on
line(xlim(), [0 0], 'Color','k', 'LineStyle',':')
line([0 0], ylim(), 'Color','k', 'LineStyle',':')
xlabel('Re(x)'), ylabel('Im(x)'), title('Roots in Complex Plane')