SharedLinear Approx to Nonlinear - Sara.sagewsOpen in CoCalc
var("M,S")
Mprime = 24*M-2*M^2-3*M*S
Sprime = 15*S-S^2-3*M*S
J = jacobian([Mprime,Sprime],[M,S])
show(J)
(M, S)
(4M3S+243M3S3M2S+15)\displaystyle \left(\begin{array}{rr} -4 \, M - 3 \, S + 24 & -3 \, M \\ -3 \, S & -3 \, M - 2 \, S + 15 \end{array}\right)
J36 = J.subs(M=3,S=6)
show(J36)
(69186)\displaystyle \left(\begin{array}{rr} -6 & -9 \\ -18 & -6 \end{array}\right)
J36.eigenvalues()
[-9*sqrt(2) - 6, 9*sqrt(2) - 6]
for eval in J36.eigenvalues():
    show(n(eval))
18.7279220613579\displaystyle -18.7279220613579
6.72792206135786\displaystyle 6.72792206135786