(1) identity holds for 2 <= e <= 100 (99 points; degree <= 8)
(2) sign pattern of D_e, K_e(1) < 0, and the two expressions for e(Z) - R: ok
(3) k=5: all 1 classes D of (2^1): |D(x)(4,0,4,0)| > |D(x)(4,0,4,2)|; largest ratio 0.809524 at D psi2 ()
(3) k=6: all 5 classes D of (2^2): |D(x)(4,0,4,0)| > |D(x)(4,0,4,2)|; largest ratio 0.860074 at D psi2 (0,)
(3) k=7: all 30 classes D of (2^3): |D(x)(4,0,4,0)| > |D(x)(4,0,4,2)|; largest ratio 0.889129 at D psi2 (1, 0)
(3) k=8: all 173 classes D of (2^4): |D(x)(4,0,4,0)| > |D(x)(4,0,4,2)|; largest ratio 0.906485 at D psi2 (2, 1, 0)
(4) R_k/e(Z_k): 3:0.666667, 4:0.943396, 5:0.809524, 6:0.860074, 7:0.837443, 8:0.846788, 9:0.842714, 10:0.844437, 11:0.843694, 12:0.844011, 13:0.843875, 14:0.843933, 15:0.843908, 16:0.843919, 17:0.843914, 18:0.843916, 19:0.843915, 20:0.843916, 21:0.843915, 22:0.843915 ... 60:0.843915
(5) end-relaxed class: cum_R(t) <= cum_Zv(t) for every t, 3 <= m <= 31 (max ratio 0.943396); D_t single-crossing and the reduced inequality >= 0
(6) the other right-end relaxed class: cum_R'(t) <= cum_Zv(t) for every t, 3 <= m <= 31 (max ratio 0.943396)
(7) a_R/a_Zv and cum_R/cum_Zv are nondecreasing in t for 3 <= m <= 26
time 8.0 s
exit 0
