example C10 : interpolants confirmed at p = 7/10, 61/100, 1/2: True
c(0, 1)(p) = p**2*(1476974*p**7 - 6646383*p**6 + 5584624*p**5 + 11470270*p**4 - 7435254*p**3 - 25595767*p**2 - 45417024*p + 103887360)/37324800
c(1, 1)(p) = -p*(p - 1)*(2*p - 1)*(25075775*p**6 - 75227325*p**5 - 1204013127*p**4 + 2533405129*p**3 - 525626577*p**2 - 753613875*p - 250047000)/250047000
c(1, 2)(p) = p**2*(p - 1)**2*(2*p - 1)*(80905*p**4 - 161810*p**3 - 5274599*p**2 + 5355504*p + 5556600)/1587600
c(2, 1)(p) = p**2*(p - 1)**2*(2*p - 1)*(212089*p**4 - 424178*p**3 - 21132311*p**2 + 21344400*p + 8467200)/4233600
c(2, 2)(p) = -p**3*(p - 1)**3*(2*p - 1)*(17*p**2 - 17*p + 420)/560
c(3, 1)(p) = 5*p**2*(p - 1)**2*(2*p - 1)*(2*p**4 - 4*p**3 - 52*p**2 + 54*p + 27)/162
c(4, 1)(p) = p**2*(p - 1)**2*(2*p - 1)*(1620701*p**4 - 3241402*p**3 - 26324299*p**2 + 27945000*p + 5400000)/38880000
c(4, 2)(p) = -p**2*(p - 1)**2*(2*p - 1)*(12929*p**4 - 25858*p**3 - 2525071*p**2 + 2538000*p + 432000)/1296000
c(4, 3)(p) = p**3*(p - 1)**3*(2*p - 1)*(1151*p**2 - 1151*p + 10800)/21600
c(5, 1)(p) = p**2*(p - 1)**2*(2*p - 1)*(2101*p**4 - 4202*p**3 + 26365*p**2 - 24264*p - 1890)/10800
c(5, 2)(p) = 7*p**3*(p - 1)**3*(2*p - 1)/5
c(6, 1)(p) = -p**3*(p - 1)**3*(2*p - 1)*(14050*p**2 - 14050*p - 11979)/81000
c(6, 2)(p) = -p**3*(p - 1)**3*(2*p - 1)*(255*p**2 - 255*p - 26)/600
c(7, 1)(p) = -433*p**4*(p - 1)**4*(2*p - 1)/6075
c(8, 1)(p) = -736145*p**4*(p - 1)**4*(2*p - 1)/6322176
c(8, 2)(p) = 8335*p**4*(p - 1)**4*(2*p - 1)/112896
c(9, 1)(p) = 31655083*p**4*(p - 1)**4*(2*p - 1)/357210000
c(9, 2)(p) = 47057*p**4*(p - 1)**4*(2*p - 1)/1134000
c(10, 1)(p) = 11677*p**4*(p - 1)**4*(2*p - 1)/2332800
real roots of c(1,2) numerator in (1/2,1): []
sign of c(1,2) on (0.5000000000, 1.000000000): 1
