E(Y) = -2*Y**5/25 + 3*Y**4/10 + 2*Y**3/5 - 8*Y**2/5 - 8*Y/5 + 209/50
equals the quintic of the claim: True
coefficients (high to low): ['-2/25', '3/10', '2/5', '-8/5', '-8/5', '209/50']
Sturm: E - 0 on (1, 9/4]: 0 distinct real roots;  value at 1: 8/5, at 9/4: 143/1280;  gcd(p, p') degree 0
Sturm: E - 1/100 on (1, 9/4]: 0 distinct real roots;  value at 1: 159/100, at 9/4: 651/6400;  gcd(p, p') degree 0
Sturm: E - 1/51 on (1, 9/4]: 0 distinct real roots;  value at 1: 403/255, at 9/4: 6013/65280;  gcd(p, p') degree 0
Sturm: E - 1/50 on (1, 9/4]: 1 distinct real roots;  value at 1: 79/50, at 9/4: 587/6400;  gcd(p, p') degree 1
Sturm: E - 1/49 on (1, 9/4]: 2 distinct real roots;  value at 1: 387/245, at 9/4: 5727/62720;  gcd(p, p') degree 0
E'(2) = 0   E(2) = 1/50   E''(2) = 16/5
Sturm: E' has 1 distinct real roots in (1, 9/4]  (E'(1) = -14/5, E'(9/4) = 443/640)
E(1) = 8/5, E(sqrt5) ~ 0.102291, E(9/4) = 143/1280
interval subdivision: |E'| <= 24829/640 = 38.795 on [1, 9/4]; 4000 pieces; certified lower bound for min E on [1, 9/4]: 16131/2048000 = 0.007876
direct quadrature of (C) at s = i/200: max |slack - sqrt(gamma) E(sqrt(1+4s))| = 1.7965e-30
  first inequality:  min slack 0.0141421356237 at s = 0.75   (sqrt(gamma)/50 = 0.0141421356237)
  second inequality: min slack 0.0141421356237 at s = 0.25
