# python3 rep10_majorant.py 6 20 1   (exact: Fractions, and D-scaled integer arithmetic for k = 4; time output from bash 'time')
ok: rep10: pi_+ vanishes exactly at ++- (so the admissible majorants are h + t 1_{++-}, t >= 0)
ok: rep10: h(++-) = -1, so h + t 1_{++-} is positive at the constant decoder (1, 1, -1) iff t > 1
   t = 1: E h_t(Y) at the constant decoder F_p = 1, F_s = -1 (k = 0) is 0
   t = 5/4: E h_t(Y) at the constant decoder F_p = 1, F_s = -1 (k = 0) is 1/4
ok: h'' = h + 1_{++-}: 8h'' = -1 - y1y2 - y1y3 + y2y3 - 2y1y2y3
   h'' at +++,++-,...,---: ['-1/2', '0', '0', '0', '1/2', '-1/2', '-1/2', '0']
ok: -8h'' = 4(1_{+++} + 1_{-+-} + 1_{--+} - 1_{-++}) (the vertex -++ against its three neighbours)
ok: -2 E h''(Y) = E[Q1P2] + E[Q1B3] + E[P2B3] - 4E[Q1P2B3] (Q = 1 - P, B = (1 + F_s)/2), 56 exact random tests with [0,1]-valued P and B, k <= 3, all nu
ok: 4 max over all {-1,1}-valued F_s of E h''(Y) = 2(L'' - R'') and L'' - R'' >= L - R, 56 exact random tests, k <= 3, all nu
rep10 majorant nu=(+4,-0): D = 20736; max (L'' - R'') = 0; L'' = R'' for 10 of 65536 P; largest negative value -0.0183256
   equality cases: 0, z1=1, z2=1, z3=1, z4=1, z4=-1, z3=-1, z2=-1, z1=-1, 1
rep10 majorant nu=(+3,-1): D = 34560; max (L'' - R'') = 0; L'' = R'' for 8 of 65536 P; largest negative value -0.0207176
   equality cases: 0, z1=1, z2=1, z3=1, z3=-1, z2=-1, z1=-1, 1
rep10 majorant nu=(+2,-2): D = 57600; max (L'' - R'') = 0; L'' = R'' for 6 of 65536 P; largest negative value -0.025
   equality cases: 0, z1=1, z2=1, z2=-1, z1=-1, 1
rep10 majorant nu=(+1,-3): D = 96000; max (L'' - R'') = 0; L'' = R'' for 4 of 65536 P; largest negative value -0.0342812
   equality cases: 0, z1=1, z1=-1, 1
rep10 majorant nu=(+0,-4): D = 160000; max (L'' - R'') = 0; L'' = R'' for 2 of 65536 P; largest negative value -0.0371
   equality cases: 0, 1
ok: rep10 majorant: L'' <= R'' for every {0,1}-valued P with k = 4 and every nu (max L'' - R'' = 0); 20 cross-checks per nu against the Fraction computation agree

real	3m27.293s
user	3m32.329s
sys	0m0.260s
