I1 n=3 Jacobiator for arbitrary F,G,H, symbolic a,b,c, simplifies to 0: True
I1 n=4 Jacobiator on coordinate triples, symbolic lambda_ij: all zero = True
I1 n=5 Jacobiator on coordinate triples, symbolic lambda_ij: all zero = True
I2 Poisson matrix A = [[0, a*x*y, -c*x*z], [-a*x*y, 0, b*y*z], [c*x*z, -b*y*z, 0]]
I2 det A = 0 ; A*kappa = [[0, 0, 0]]
I2 2x2 minors of A (gcd of all): 1
I3 {F,G} - det[grad F, grad G, kappa] == 0 for arbitrary F,G: True
I4 minpoly(sqrt2+sqrt3) = X**4 - 10*X**2 + 1 ; factor_list over Q: (1, [(X**4 - 10*X**2 + 1, 1)])
I4 det of conjugate matrix of (1,s2,s3,s6) = -96 (nonzero and degree 4 => Q-basis, so 1,s2,s3 Q-independent)
I4 factor_list(X^6-2) over Q: (1, [(X**6 - 2, 1)]) (Eisenstein at 2 as well)
I4 Pf(lambda) for Theorem D = 2**(5/6) = 2**(5/6) ; equals theta^5: True
I4 det(D L4 D) - theta^10 (x1x2x3x4)^2 == 0: True
I5 Jacobiator of phi*pi0 on (x,y,z), arbitrary phi, symbolic a,b,c: [0]
I6 {x^al,x^be}/x^(al+be) - lambda(al,be) == 0: True ; lambda(al,be) - (b,c,a).(al x be) == 0: True
total 0.3s
