generic Sylvester determinant: 13 terms
PASS (1) A^2 * Syl = lam^2 C - lam mu B + A mu^2  (so Syl = A^3 g(rho1) g(rho2))
R(a,b,c): 10426 terms, total degrees 18..45, content 4  [5.0s]
P_2 coefficient sizes (r^0, r^1, r^2): [64, 59, 64]  P_3: [278, 296, 296, 278]
PASS (2) R has 10426 terms, total degrees 18..45 and content 4
PASS (3) R(a,b,c) = D_2^3 D_3^2 Res(M_2, M_3) at 60 random rational points
R1(u,v,w): 3290 terms, total degrees 0..27, content of 4*R1 = 4, constant term 29  [27.0s]
PASS (4) R(u,u+v,u+v+w) = 4 (vw(v+w))^6 R1 exactly
PASS (4) all 3290 coefficients of R1 are nonnegative, R1(0,0,0) = 29
R2(u,v,w): 3115 terms, total degrees 6..27, content of 4*R2 = 91507169819844
   lowest pure-u term of R2: u^6 with coefficient 3335436339933313800000 = 3^45 * 200000/177147  [37.4s]
PASS (5) 3^45 R(-1/3+u, -1/3+u+v, -1/3+u+v+w) = 4 (vw(v+w))^6 R2 exactly
PASS (5) all 3115 coefficients of R2 are nonnegative, lowest pure-u term is kappa u^6 with kappa > 0
R(u,u+1+v,u+2+v+w): 13400 terms, constant term 82556485632000  [44.7s]
PASS (6) all 13400 coefficients are nonnegative, constant term 82556485632000 = 4*20639121408000
PASS (7) coordinate versions agree with R(a,b,c) at 20 random points each
PASS (8) gcd(M_2(r), M_3(r)) = 1 for all 2300 integer triples 0 <= a < b < c <= 24
wrote R1_uvw.txt (3290 terms)
ALL CHECKS PASSED  total time 52.5s
