difference numerator: (u - 1)**6*(u + 1)**10
number of real roots of the numerator in (1, oo): 1  ; at u = 1 (circle): 0
denominator: u*(u**2 + 1)*(u**2 + u + 1)*(u**2 + 4*u + 1)  (positive for u > 0)
N=6 kappa_6 = A*_f1/A      = (-a + 2*b)*(a + b)**2/(b**2*(2*a + b))   [guess in (a,b) agrees exactly: True]
N=6 A' A*_f1               = 4*a**2*(-a**2 + 4*b**2)   [guess in (a,b) agrees exactly: True]
N=6 A' A                   = 4*a**2*b**2*(a + 2*b)*(2*a + b)/(a + b)**2   [guess in (a,b) agrees exactly: True]
N=6 A/A_f1 (k204)          = (a + b)**2/(a*(2*a + b))   [guess in (a,b) agrees exactly: True]
N=6 A/A_O (k204)           = (a + b)**2/(a**2 + a*b + b**2)   [guess in (a,b) agrees exactly: True]
N=6 A*_f1/A_f1 (k404)      = (-a + 2*b)*(a + b)**4/(a*b**2*(2*a + b)**2)   [guess in (a,b) agrees exactly: True]
N=6 A'/A'' (k113)          = (a + b)**4/(a*b*(a + 2*b)*(2*a + b))   [guess in (a,b) agrees exactly: True]
N=6 A'A'_O (k303a)         = a*b*(a + 2*b)*(2*a + b)   [guess in (a,b) agrees exactly: True]
N=4 A' A*_f1               = 16*a**2*b**2   [guess in (a,b) agrees exactly: True]
N=4 A' A                   = 8*a**2*b**2   [guess in (a,b) agrees exactly: True]
N=4 A_f1 A*_f1 (k403b)     = 16*a**4*b**4/(a**2 + b**2)**2   [guess in (a,b) agrees exactly: True]
