P_2 coefficient term counts r^0..r^2: [64, 59, 64] (paper: 64, 59, 64)
P_3 coefficient term counts r^0..r^3: [278, 296, 296, 278] (paper: 278, 296, 296, 278)
R(e1,e2,e3): 10426 terms, total degrees 18..45, content 4  (paper: 10426, 18..45, 4)  [1.0s]
R vs exact 5x5 Sylvester determinant (4) at 30 random integer points: 0 mismatches
R vs D_2^3 D_3^2 Res(M_2,M_3) (integral formula, Fractions) at random rational triples: 0 mismatches
(i) substituted resultant built from scratch: 5636 terms; agrees with S^45 R(e) at 15 random points: 0 mismatches [1.2s]
(iii) substituted resultant built from scratch: 13400 terms; agrees with S^45 R(e) at 15 random points: 0 mismatches [2.3s]
(ii) substituted resultant built from scratch: 5299 terms; agrees with S^45 R(e) at 15 random points: 0 mismatches [0.9s]
(i) R(u,u+v,u+v+w) = 4 (vw(v+w))^6 R1 exactly (multiplied back: True); R1: 3290 terms, degrees 0..27, all coefficients positive integers: True, R1(0,0,0) = 29, content 1  (paper: 3290 terms, 0..27, R1(0,0,0) = 29)
(iii) R(u,u+1+v,u+2+v+w): 13400 terms, degrees 0..45, all coefficients positive: True, constant term 82556485632000 = 4*20639121408000, content 4  (paper: 13400 terms, positive, constant 82556485632000)
     direct check: R(0,1,2) = 82556485632000
(ii) 3^45 R(-1/3+u, ...) = (VW(V+W))^6 Q exactly (multiplied back: True); R2 = R/(4(vw(v+w))^6): 3115 terms, degrees 6..27, all coefficients positive: True
     pure-u part of R2: lowest term 200000/177147 u^6 (paper: 200000/177147 u^6); pure-u degrees 6..27, all positive: True
     monomials of lowest total degree 6: 28; does R2 contain u^6 exactly as a monomial: True
total time 7.0s
