tangency residuals: [0, 0, 0, 0]
A_pol/A^dag  = 2*a**4/b**4
A_pol/A_dual = 2*a**6/b**10
A_ped/A_dual = 2*a**6/(b**2*(a**2 + b**2)**2)
A*A^dag      = 4
A_ant/A      = 2
