(1) a^2 - b^2 - c^2 = 0
(1) a^2 - lam - a''^2 = 0 ; b^2 - lam - b''^2 = 0
(1) 2 - mu* - R = 0
(1) R - Rhand = 0
(2) kappa_4 = 2 ; kappa_6 = -(a - 2*b)*(a + b)**2/(b**2*(2*a + b)) ; equals claimed: True
(3) orbit I: on e [0, 0, 0, 0, 0, 0]; tangency residuals [0, 0, 0, 0, 0, 0]
    A = 2*a*b**(3/2)*(2*a + b)**(3/2)/(a + b)**2; A' = 2*a*sqrt(b)*(a + 2*b)/sqrt(2*a + b); A*_O = 2*a*(a**3 - 2*a**2*b + 2*a*b**2 + 2*b**3)/(b**(3/2)*sqrt(2*a + b))
    A*_f1 - A*_f2 = 0; A*_f1/A - kappa6 = 0
    A'A = 4*a**2*b**2*(a + 2*b)*(2*a + b)/(a + b)**2; A'A*_f1 = -4*a**2*(a - 2*b)*(a + 2*b); A'A*_O = 4*a**2*(a + 2*b)*(a**3 - 2*a**2*b + 2*a*b**2 + 2*b**3)/(b*(2*a + b))
(3) orbit II: on e [0, 0, 0, 0, 0, 0]; tangency residuals [0, 0, 0, 0, 0, 0]
    A = 2*a**(3/2)*b*(a + 2*b)**(3/2)/(a + b)**2; A' = 2*sqrt(a)*b*(2*a + b)/sqrt(a + 2*b); A*_O = 2*b*(2*a**3 + 2*a**2*b - 2*a*b**2 + b**3)/(a**(3/2)*sqrt(a + 2*b))
    A*_f1 - A*_f2 = 0; A*_f1/A - kappa6 = 0
    A'A = 4*a**2*b**2*(a + 2*b)*(2*a + b)/(a + b)**2; A'A*_f1 = -4*a**2*(a - 2*b)*(a + 2*b); A'A*_O = 4*b**2*(2*a + b)*(2*a**3 + 2*a**2*b - 2*a*b**2 + b**3)/(a*(a + 2*b))
(3) A'A*_O(I) - A'A*_O(II) = 4*(a - b)**3*(a + b)**5/(a*b*(a + 2*b)*(2*a + b))
(3) minus claimed 4(a-b)^3(a+b)^5/(ab(2a+b)(a+2b)) : 0
(3) at a=8/5,b=1: 371293/87500
nice -n 10 python -I   1.59s user 0.03s system 99% cpu 1.630 total
