/* Example 3D system. Linear stability analysis of the origin. */
f: a*x+b*y+r*z+c*y^3;
g: d*x+k*y-m*x^2;
h: n*x+p*y-j*z;

/* Maxima may not find Eq. Pts well! Maple and Mathematica might do a better job, or do BY HAND. */
solve([f,g,h],[x,y,z]);

J: jacobian([f,g,h],[x,y,z]);
J0:J,x=0,y=0,z=0;

cp:-determinant(J0-matrix([L,0,0],[0,L,0],[0,0,L]));

cp:expand(cp);

a1:coeff(cp,L,2);

a2:coeff(cp,L,1);

a3:cp,L=0;

/* Apply Routh-Hurwitz Stability Criteria */
a1>0;

a1+k+a>k+a; /* Rearrange to something a little more meaninful */;

a3>0;

a1*a2>a3;

/* Compare to the stability analysis based on finding the eigenvalues of J0 */
eigenvalues(J0);