mmcdara

1247 Reputation

13 Badges

4 years, 72 days

MaplePrimes Activity


These are replies submitted by mmcdara

@SeyiOshin 

Do you have any idea how complex can be the expressions of the eigenvalues of a general square matrix (and thus of the time and the memory required to buid these expressions) ?

The first example concerns the computations of the eigenvalues of a formal squre matrix.
The second the computations of the eigenvalues of a matrix of integers.
The third one the computations of the eigenvalues of a matrix of floats (basically what Matlab does, unless you use its Symbolic Toolbox).

Another point that the second example illustrate: the eigenvalues are the roots of some polynomial and it's known that no general expression does exist to express the roots of any polynomial of order larger than 4.
Of course this problem does not exist for matrix of floats.


Now, if you want to assess the derivative of an eigenvalue V[k] to the element M[i,j] of some matrix M, a simple thing to do (unless your matrix has small size and/or has a "simple" structure)  is to compute
(V'[k]-V[k]) / ((M[i,j]+eps) - M[i,j])  for |eps| "small"
where V'[k] is the corresponding kth eigenvalue of the matrix M' which differs from M only by its [i,j] term now equal to M[i,j]+eps

More cleverly you can also use theorirical results about the eigenvalues of M'=M+eps*E (for |eps| small again) :
V'(k) = V(k) + eps*(vT[k].E.u[k]) where vT[k] and u[k] are the right and left kth eigenvectors of M
'here E could the matrix E[i', j']=1 if i'=' and j=j' and 0 otherwise)


 

restart

with(LinearAlgebra):

for N from 2 to 4 do
  M       := Matrix(N$2, symbol=s):
  eig_||N := CodeTools:-Usage( Eigenvalues(M) ):
  print(length(eig_||N)):  # length(eig_||N) returns the number of words used to represent eig_||N
end do:

memory used=3.70MiB, alloc change=32.00MiB, cpu time=162.00ms, real time=7.10s, gc time=7.54ms

 

302

 

memory used=7.41MiB, alloc change=0 bytes, cpu time=117.00ms, real time=5.73s, gc time=0ns

 

87720

 

memory used=3.16GiB, alloc change=407.25MiB, cpu time=50.70s, real time=36.18s, gc time=23.98s

 

174243014

(1)

eig_3;  # eigenvalues of a 3 by 3 matrix with generic element s[i,j]

Vector(3, {(1) = (1/6)*(8*s[1, 1]^3-12*s[1, 1]^2*s[2, 2]-12*s[1, 1]^2*s[3, 3]+36*s[1, 1]*s[1, 2]*s[2, 1]+36*s[1, 1]*s[1, 3]*s[3, 1]-12*s[1, 1]*s[2, 2]^2+48*s[1, 1]*s[2, 2]*s[3, 3]-72*s[1, 1]*s[2, 3]*s[3, 2]-12*s[1, 1]*s[3, 3]^2+36*s[1, 2]*s[2, 1]*s[2, 2]-72*s[1, 2]*s[2, 1]*s[3, 3]+108*s[1, 2]*s[2, 3]*s[3, 1]+108*s[1, 3]*s[2, 1]*s[3, 2]-72*s[1, 3]*s[2, 2]*s[3, 1]+36*s[1, 3]*s[3, 1]*s[3, 3]+8*s[2, 2]^3-12*s[2, 2]^2*s[3, 3]+36*s[2, 2]*s[2, 3]*s[3, 2]-12*s[2, 2]*s[3, 3]^2+36*s[2, 3]*s[3, 2]*s[3, 3]+8*s[3, 3]^3+12*sqrt(-3*s[1, 1]^4*s[2, 2]^2+6*s[1, 1]^4*s[2, 2]*s[3, 3]-12*s[1, 1]^4*s[2, 3]*s[3, 2]-3*s[1, 1]^4*s[3, 3]^2+6*s[1, 1]^3*s[1, 2]*s[2, 1]*s[2, 2]-6*s[1, 1]^3*s[1, 2]*s[2, 1]*s[3, 3]+12*s[1, 1]^3*s[1, 2]*s[2, 3]*s[3, 1]+12*s[1, 1]^3*s[1, 3]*s[2, 1]*s[3, 2]-6*s[1, 1]^3*s[1, 3]*s[2, 2]*s[3, 1]+6*s[1, 1]^3*s[1, 3]*s[3, 1]*s[3, 3]+6*s[1, 1]^3*s[2, 2]^3-6*s[1, 1]^3*s[2, 2]^2*s[3, 3]+24*s[1, 1]^3*s[2, 2]*s[2, 3]*s[3, 2]-6*s[1, 1]^3*s[2, 2]*s[3, 3]^2+24*s[1, 1]^3*s[2, 3]*s[3, 2]*s[3, 3]+6*s[1, 1]^3*s[3, 3]^3-3*s[1, 1]^2*s[1, 2]^2*s[2, 1]^2-6*s[1, 1]^2*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]-24*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 2]^2+30*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]-60*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]-6*s[1, 1]^2*s[1, 2]*s[2, 1]*s[3, 3]^2-18*s[1, 1]^2*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]-18*s[1, 1]^2*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]-3*s[1, 1]^2*s[1, 3]^2*s[3, 1]^2-18*s[1, 1]^2*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]-18*s[1, 1]^2*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]-6*s[1, 1]^2*s[1, 3]*s[2, 2]^2*s[3, 1]+30*s[1, 1]^2*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]-60*s[1, 1]^2*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]-24*s[1, 1]^2*s[1, 3]*s[3, 1]*s[3, 3]^2-3*s[1, 1]^2*s[2, 2]^4-6*s[1, 1]^2*s[2, 2]^3*s[3, 3]-6*s[1, 1]^2*s[2, 2]^2*s[2, 3]*s[3, 2]+18*s[1, 1]^2*s[2, 2]^2*s[3, 3]^2-60*s[1, 1]^2*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]-6*s[1, 1]^2*s[2, 2]*s[3, 3]^3+24*s[1, 1]^2*s[2, 3]^2*s[3, 2]^2-6*s[1, 1]^2*s[2, 3]*s[3, 2]*s[3, 3]^2-3*s[1, 1]^2*s[3, 3]^4+30*s[1, 1]*s[1, 2]^2*s[2, 1]^2*s[2, 2]-24*s[1, 1]*s[1, 2]^2*s[2, 1]^2*s[3, 3]+54*s[1, 1]*s[1, 2]^2*s[2, 1]*s[2, 3]*s[3, 1]+54*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]^2*s[3, 2]+6*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 1]+6*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]*s[3, 3]+54*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 3]*s[3, 1]^2+6*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]^3+30*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]^2*s[3, 3]+6*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]-60*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]^2+114*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]*s[3, 3]+24*s[1, 1]*s[1, 2]*s[2, 1]*s[3, 3]^3-18*s[1, 1]*s[1, 2]*s[2, 2]^2*s[2, 3]*s[3, 1]+72*s[1, 1]*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 3]-108*s[1, 1]*s[1, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]-18*s[1, 1]*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]^2+54*s[1, 1]*s[1, 3]^2*s[2, 1]*s[3, 1]*s[3, 2]-24*s[1, 1]*s[1, 3]^2*s[2, 2]*s[3, 1]^2+30*s[1, 1]*s[1, 3]^2*s[3, 1]^2*s[3, 3]-18*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 2]+72*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]*s[3, 3]-108*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 2]^2-18*s[1, 1]*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]^2+24*s[1, 1]*s[1, 3]*s[2, 2]^3*s[3, 1]-60*s[1, 1]*s[1, 3]*s[2, 2]^2*s[3, 1]*s[3, 3]+114*s[1, 1]*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 2]+30*s[1, 1]*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]^2+6*s[1, 1]*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]+6*s[1, 1]*s[1, 3]*s[3, 1]*s[3, 3]^3+6*s[1, 1]*s[2, 2]^4*s[3, 3]-6*s[1, 1]*s[2, 2]^3*s[2, 3]*s[3, 2]-6*s[1, 1]*s[2, 2]^3*s[3, 3]^2+30*s[1, 1]*s[2, 2]^2*s[2, 3]*s[3, 2]*s[3, 3]-6*s[1, 1]*s[2, 2]^2*s[3, 3]^3-24*s[1, 1]*s[2, 2]*s[2, 3]^2*s[3, 2]^2+30*s[1, 1]*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]^2+6*s[1, 1]*s[2, 2]*s[3, 3]^4-24*s[1, 1]*s[2, 3]^2*s[3, 2]^2*s[3, 3]-6*s[1, 1]*s[2, 3]*s[3, 2]*s[3, 3]^3-12*s[1, 2]^3*s[2, 1]^3-36*s[1, 2]^2*s[1, 3]*s[2, 1]^2*s[3, 1]-3*s[1, 2]^2*s[2, 1]^2*s[2, 2]^2-24*s[1, 2]^2*s[2, 1]^2*s[2, 2]*s[3, 3]-36*s[1, 2]^2*s[2, 1]^2*s[2, 3]*s[3, 2]+24*s[1, 2]^2*s[2, 1]^2*s[3, 3]^2+54*s[1, 2]^2*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 1]-108*s[1, 2]^2*s[2, 1]*s[2, 3]*s[3, 1]*s[3, 3]+81*s[1, 2]^2*s[2, 3]^2*s[3, 1]^2-36*s[1, 2]*s[1, 3]^2*s[2, 1]*s[3, 1]^2+54*s[1, 2]*s[1, 3]*s[2, 1]^2*s[2, 2]*s[3, 2]-108*s[1, 2]*s[1, 3]*s[2, 1]^2*s[3, 2]*s[3, 3]-60*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 1]+114*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 1]*s[3, 3]+90*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 1]*s[3, 2]-60*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]*s[3, 3]^2-108*s[1, 2]*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]^2+54*s[1, 2]*s[1, 3]*s[2, 3]*s[3, 1]^2*s[3, 3]-6*s[1, 2]*s[2, 1]*s[2, 2]^3*s[3, 3]-6*s[1, 2]*s[2, 1]*s[2, 2]^2*s[2, 3]*s[3, 2]-6*s[1, 2]*s[2, 1]*s[2, 2]^2*s[3, 3]^2+6*s[1, 2]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]+24*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]^3-36*s[1, 2]*s[2, 1]*s[2, 3]^2*s[3, 2]^2-60*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]*s[3, 3]^2-12*s[1, 2]*s[2, 1]*s[3, 3]^4+12*s[1, 2]*s[2, 2]^3*s[2, 3]*s[3, 1]-18*s[1, 2]*s[2, 2]^2*s[2, 3]*s[3, 1]*s[3, 3]+54*s[1, 2]*s[2, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]-18*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 3]^2+54*s[1, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]*s[3, 3]+12*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]^3-12*s[1, 3]^3*s[3, 1]^3+81*s[1, 3]^2*s[2, 1]^2*s[3, 2]^2-108*s[1, 3]^2*s[2, 1]*s[2, 2]*s[3, 1]*s[3, 2]+54*s[1, 3]^2*s[2, 1]*s[3, 1]*s[3, 2]*s[3, 3]+24*s[1, 3]^2*s[2, 2]^2*s[3, 1]^2-24*s[1, 3]^2*s[2, 2]*s[3, 1]^2*s[3, 3]-36*s[1, 3]^2*s[2, 3]*s[3, 1]^2*s[3, 2]-3*s[1, 3]^2*s[3, 1]^2*s[3, 3]^2+12*s[1, 3]*s[2, 1]*s[2, 2]^3*s[3, 2]-18*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 2]*s[3, 3]+54*s[1, 3]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]^2-18*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]*s[3, 3]^2+54*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 2]^2*s[3, 3]+12*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]^3-12*s[1, 3]*s[2, 2]^4*s[3, 1]+24*s[1, 3]*s[2, 2]^3*s[3, 1]*s[3, 3]-60*s[1, 3]*s[2, 2]^2*s[2, 3]*s[3, 1]*s[3, 2]-6*s[1, 3]*s[2, 2]^2*s[3, 1]*s[3, 3]^2+6*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]-6*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]^3-36*s[1, 3]*s[2, 3]^2*s[3, 1]*s[3, 2]^2-6*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]^2-3*s[2, 2]^4*s[3, 3]^2+6*s[2, 2]^3*s[2, 3]*s[3, 2]*s[3, 3]+6*s[2, 2]^3*s[3, 3]^3-3*s[2, 2]^2*s[2, 3]^2*s[3, 2]^2-24*s[2, 2]^2*s[2, 3]*s[3, 2]*s[3, 3]^2-3*s[2, 2]^2*s[3, 3]^4+30*s[2, 2]*s[2, 3]^2*s[3, 2]^2*s[3, 3]+6*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]^3-12*s[2, 3]^3*s[3, 2]^3-3*s[2, 3]^2*s[3, 2]^2*s[3, 3]^2))^(1/3)-((2/3)*s[1, 1]*s[2, 2]+(2/3)*s[3, 3]*s[1, 1]-2*s[1, 2]*s[2, 1]-2*s[1, 3]*s[3, 1]+(2/3)*s[3, 3]*s[2, 2]-2*s[2, 3]*s[3, 2]-(2/3)*s[1, 1]^2-(2/3)*s[2, 2]^2-(2/3)*s[3, 3]^2)/(8*s[1, 1]^3-12*s[1, 1]^2*s[2, 2]-12*s[1, 1]^2*s[3, 3]+36*s[1, 1]*s[1, 2]*s[2, 1]+36*s[1, 1]*s[1, 3]*s[3, 1]-12*s[1, 1]*s[2, 2]^2+48*s[1, 1]*s[2, 2]*s[3, 3]-72*s[1, 1]*s[2, 3]*s[3, 2]-12*s[1, 1]*s[3, 3]^2+36*s[1, 2]*s[2, 1]*s[2, 2]-72*s[1, 2]*s[2, 1]*s[3, 3]+108*s[1, 2]*s[2, 3]*s[3, 1]+108*s[1, 3]*s[2, 1]*s[3, 2]-72*s[1, 3]*s[2, 2]*s[3, 1]+36*s[1, 3]*s[3, 1]*s[3, 3]+8*s[2, 2]^3-12*s[2, 2]^2*s[3, 3]+36*s[2, 2]*s[2, 3]*s[3, 2]-12*s[2, 2]*s[3, 3]^2+36*s[2, 3]*s[3, 2]*s[3, 3]+8*s[3, 3]^3+12*sqrt(-3*s[1, 1]^4*s[2, 2]^2+6*s[1, 1]^4*s[2, 2]*s[3, 3]-12*s[1, 1]^4*s[2, 3]*s[3, 2]-3*s[1, 1]^4*s[3, 3]^2+6*s[1, 1]^3*s[1, 2]*s[2, 1]*s[2, 2]-6*s[1, 1]^3*s[1, 2]*s[2, 1]*s[3, 3]+12*s[1, 1]^3*s[1, 2]*s[2, 3]*s[3, 1]+12*s[1, 1]^3*s[1, 3]*s[2, 1]*s[3, 2]-6*s[1, 1]^3*s[1, 3]*s[2, 2]*s[3, 1]+6*s[1, 1]^3*s[1, 3]*s[3, 1]*s[3, 3]+6*s[1, 1]^3*s[2, 2]^3-6*s[1, 1]^3*s[2, 2]^2*s[3, 3]+24*s[1, 1]^3*s[2, 2]*s[2, 3]*s[3, 2]-6*s[1, 1]^3*s[2, 2]*s[3, 3]^2+24*s[1, 1]^3*s[2, 3]*s[3, 2]*s[3, 3]+6*s[1, 1]^3*s[3, 3]^3-3*s[1, 1]^2*s[1, 2]^2*s[2, 1]^2-6*s[1, 1]^2*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]-24*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 2]^2+30*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]-60*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]-6*s[1, 1]^2*s[1, 2]*s[2, 1]*s[3, 3]^2-18*s[1, 1]^2*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]-18*s[1, 1]^2*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]-3*s[1, 1]^2*s[1, 3]^2*s[3, 1]^2-18*s[1, 1]^2*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]-18*s[1, 1]^2*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]-6*s[1, 1]^2*s[1, 3]*s[2, 2]^2*s[3, 1]+30*s[1, 1]^2*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]-60*s[1, 1]^2*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]-24*s[1, 1]^2*s[1, 3]*s[3, 1]*s[3, 3]^2-3*s[1, 1]^2*s[2, 2]^4-6*s[1, 1]^2*s[2, 2]^3*s[3, 3]-6*s[1, 1]^2*s[2, 2]^2*s[2, 3]*s[3, 2]+18*s[1, 1]^2*s[2, 2]^2*s[3, 3]^2-60*s[1, 1]^2*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]-6*s[1, 1]^2*s[2, 2]*s[3, 3]^3+24*s[1, 1]^2*s[2, 3]^2*s[3, 2]^2-6*s[1, 1]^2*s[2, 3]*s[3, 2]*s[3, 3]^2-3*s[1, 1]^2*s[3, 3]^4+30*s[1, 1]*s[1, 2]^2*s[2, 1]^2*s[2, 2]-24*s[1, 1]*s[1, 2]^2*s[2, 1]^2*s[3, 3]+54*s[1, 1]*s[1, 2]^2*s[2, 1]*s[2, 3]*s[3, 1]+54*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]^2*s[3, 2]+6*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 1]+6*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]*s[3, 3]+54*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 3]*s[3, 1]^2+6*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]^3+30*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]^2*s[3, 3]+6*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]-60*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]^2+114*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]*s[3, 3]+24*s[1, 1]*s[1, 2]*s[2, 1]*s[3, 3]^3-18*s[1, 1]*s[1, 2]*s[2, 2]^2*s[2, 3]*s[3, 1]+72*s[1, 1]*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 3]-108*s[1, 1]*s[1, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]-18*s[1, 1]*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]^2+54*s[1, 1]*s[1, 3]^2*s[2, 1]*s[3, 1]*s[3, 2]-24*s[1, 1]*s[1, 3]^2*s[2, 2]*s[3, 1]^2+30*s[1, 1]*s[1, 3]^2*s[3, 1]^2*s[3, 3]-18*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 2]+72*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]*s[3, 3]-108*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 2]^2-18*s[1, 1]*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]^2+24*s[1, 1]*s[1, 3]*s[2, 2]^3*s[3, 1]-60*s[1, 1]*s[1, 3]*s[2, 2]^2*s[3, 1]*s[3, 3]+114*s[1, 1]*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 2]+30*s[1, 1]*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]^2+6*s[1, 1]*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]+6*s[1, 1]*s[1, 3]*s[3, 1]*s[3, 3]^3+6*s[1, 1]*s[2, 2]^4*s[3, 3]-6*s[1, 1]*s[2, 2]^3*s[2, 3]*s[3, 2]-6*s[1, 1]*s[2, 2]^3*s[3, 3]^2+30*s[1, 1]*s[2, 2]^2*s[2, 3]*s[3, 2]*s[3, 3]-6*s[1, 1]*s[2, 2]^2*s[3, 3]^3-24*s[1, 1]*s[2, 2]*s[2, 3]^2*s[3, 2]^2+30*s[1, 1]*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]^2+6*s[1, 1]*s[2, 2]*s[3, 3]^4-24*s[1, 1]*s[2, 3]^2*s[3, 2]^2*s[3, 3]-6*s[1, 1]*s[2, 3]*s[3, 2]*s[3, 3]^3-12*s[1, 2]^3*s[2, 1]^3-36*s[1, 2]^2*s[1, 3]*s[2, 1]^2*s[3, 1]-3*s[1, 2]^2*s[2, 1]^2*s[2, 2]^2-24*s[1, 2]^2*s[2, 1]^2*s[2, 2]*s[3, 3]-36*s[1, 2]^2*s[2, 1]^2*s[2, 3]*s[3, 2]+24*s[1, 2]^2*s[2, 1]^2*s[3, 3]^2+54*s[1, 2]^2*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 1]-108*s[1, 2]^2*s[2, 1]*s[2, 3]*s[3, 1]*s[3, 3]+81*s[1, 2]^2*s[2, 3]^2*s[3, 1]^2-36*s[1, 2]*s[1, 3]^2*s[2, 1]*s[3, 1]^2+54*s[1, 2]*s[1, 3]*s[2, 1]^2*s[2, 2]*s[3, 2]-108*s[1, 2]*s[1, 3]*s[2, 1]^2*s[3, 2]*s[3, 3]-60*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 1]+114*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 1]*s[3, 3]+90*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 1]*s[3, 2]-60*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]*s[3, 3]^2-108*s[1, 2]*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]^2+54*s[1, 2]*s[1, 3]*s[2, 3]*s[3, 1]^2*s[3, 3]-6*s[1, 2]*s[2, 1]*s[2, 2]^3*s[3, 3]-6*s[1, 2]*s[2, 1]*s[2, 2]^2*s[2, 3]*s[3, 2]-6*s[1, 2]*s[2, 1]*s[2, 2]^2*s[3, 3]^2+6*s[1, 2]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]+24*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]^3-36*s[1, 2]*s[2, 1]*s[2, 3]^2*s[3, 2]^2-60*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]*s[3, 3]^2-12*s[1, 2]*s[2, 1]*s[3, 3]^4+12*s[1, 2]*s[2, 2]^3*s[2, 3]*s[3, 1]-18*s[1, 2]*s[2, 2]^2*s[2, 3]*s[3, 1]*s[3, 3]+54*s[1, 2]*s[2, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]-18*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 3]^2+54*s[1, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]*s[3, 3]+12*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]^3-12*s[1, 3]^3*s[3, 1]^3+81*s[1, 3]^2*s[2, 1]^2*s[3, 2]^2-108*s[1, 3]^2*s[2, 1]*s[2, 2]*s[3, 1]*s[3, 2]+54*s[1, 3]^2*s[2, 1]*s[3, 1]*s[3, 2]*s[3, 3]+24*s[1, 3]^2*s[2, 2]^2*s[3, 1]^2-24*s[1, 3]^2*s[2, 2]*s[3, 1]^2*s[3, 3]-36*s[1, 3]^2*s[2, 3]*s[3, 1]^2*s[3, 2]-3*s[1, 3]^2*s[3, 1]^2*s[3, 3]^2+12*s[1, 3]*s[2, 1]*s[2, 2]^3*s[3, 2]-18*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 2]*s[3, 3]+54*s[1, 3]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]^2-18*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]*s[3, 3]^2+54*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 2]^2*s[3, 3]+12*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]^3-12*s[1, 3]*s[2, 2]^4*s[3, 1]+24*s[1, 3]*s[2, 2]^3*s[3, 1]*s[3, 3]-60*s[1, 3]*s[2, 2]^2*s[2, 3]*s[3, 1]*s[3, 2]-6*s[1, 3]*s[2, 2]^2*s[3, 1]*s[3, 3]^2+6*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]-6*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]^3-36*s[1, 3]*s[2, 3]^2*s[3, 1]*s[3, 2]^2-6*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]^2-3*s[2, 2]^4*s[3, 3]^2+6*s[2, 2]^3*s[2, 3]*s[3, 2]*s[3, 3]+6*s[2, 2]^3*s[3, 3]^3-3*s[2, 2]^2*s[2, 3]^2*s[3, 2]^2-24*s[2, 2]^2*s[2, 3]*s[3, 2]*s[3, 3]^2-3*s[2, 2]^2*s[3, 3]^4+30*s[2, 2]*s[2, 3]^2*s[3, 2]^2*s[3, 3]+6*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]^3-12*s[2, 3]^3*s[3, 2]^3-3*s[2, 3]^2*s[3, 2]^2*s[3, 3]^2))^(1/3)+(1/3)*s[3, 3]+(1/3)*s[2, 2]+(1/3)*s[1, 1], (2) = -(1/12)*(8*s[1, 1]^3-12*s[1, 1]^2*s[2, 2]-12*s[1, 1]^2*s[3, 3]+36*s[1, 1]*s[1, 2]*s[2, 1]+36*s[1, 1]*s[1, 3]*s[3, 1]-12*s[1, 1]*s[2, 2]^2+48*s[1, 1]*s[2, 2]*s[3, 3]-72*s[1, 1]*s[2, 3]*s[3, 2]-12*s[1, 1]*s[3, 3]^2+36*s[1, 2]*s[2, 1]*s[2, 2]-72*s[1, 2]*s[2, 1]*s[3, 3]+108*s[1, 2]*s[2, 3]*s[3, 1]+108*s[1, 3]*s[2, 1]*s[3, 2]-72*s[1, 3]*s[2, 2]*s[3, 1]+36*s[1, 3]*s[3, 1]*s[3, 3]+8*s[2, 2]^3-12*s[2, 2]^2*s[3, 3]+36*s[2, 2]*s[2, 3]*s[3, 2]-12*s[2, 2]*s[3, 3]^2+36*s[2, 3]*s[3, 2]*s[3, 3]+8*s[3, 3]^3+12*sqrt(-3*s[1, 1]^4*s[2, 2]^2+6*s[1, 1]^4*s[2, 2]*s[3, 3]-12*s[1, 1]^4*s[2, 3]*s[3, 2]-3*s[1, 1]^4*s[3, 3]^2+6*s[1, 1]^3*s[1, 2]*s[2, 1]*s[2, 2]-6*s[1, 1]^3*s[1, 2]*s[2, 1]*s[3, 3]+12*s[1, 1]^3*s[1, 2]*s[2, 3]*s[3, 1]+12*s[1, 1]^3*s[1, 3]*s[2, 1]*s[3, 2]-6*s[1, 1]^3*s[1, 3]*s[2, 2]*s[3, 1]+6*s[1, 1]^3*s[1, 3]*s[3, 1]*s[3, 3]+6*s[1, 1]^3*s[2, 2]^3-6*s[1, 1]^3*s[2, 2]^2*s[3, 3]+24*s[1, 1]^3*s[2, 2]*s[2, 3]*s[3, 2]-6*s[1, 1]^3*s[2, 2]*s[3, 3]^2+24*s[1, 1]^3*s[2, 3]*s[3, 2]*s[3, 3]+6*s[1, 1]^3*s[3, 3]^3-3*s[1, 1]^2*s[1, 2]^2*s[2, 1]^2-6*s[1, 1]^2*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]-24*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 2]^2+30*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]-60*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]-6*s[1, 1]^2*s[1, 2]*s[2, 1]*s[3, 3]^2-18*s[1, 1]^2*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]-18*s[1, 1]^2*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]-3*s[1, 1]^2*s[1, 3]^2*s[3, 1]^2-18*s[1, 1]^2*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]-18*s[1, 1]^2*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]-6*s[1, 1]^2*s[1, 3]*s[2, 2]^2*s[3, 1]+30*s[1, 1]^2*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]-60*s[1, 1]^2*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]-24*s[1, 1]^2*s[1, 3]*s[3, 1]*s[3, 3]^2-3*s[1, 1]^2*s[2, 2]^4-6*s[1, 1]^2*s[2, 2]^3*s[3, 3]-6*s[1, 1]^2*s[2, 2]^2*s[2, 3]*s[3, 2]+18*s[1, 1]^2*s[2, 2]^2*s[3, 3]^2-60*s[1, 1]^2*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]-6*s[1, 1]^2*s[2, 2]*s[3, 3]^3+24*s[1, 1]^2*s[2, 3]^2*s[3, 2]^2-6*s[1, 1]^2*s[2, 3]*s[3, 2]*s[3, 3]^2-3*s[1, 1]^2*s[3, 3]^4+30*s[1, 1]*s[1, 2]^2*s[2, 1]^2*s[2, 2]-24*s[1, 1]*s[1, 2]^2*s[2, 1]^2*s[3, 3]+54*s[1, 1]*s[1, 2]^2*s[2, 1]*s[2, 3]*s[3, 1]+54*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]^2*s[3, 2]+6*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 1]+6*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]*s[3, 3]+54*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 3]*s[3, 1]^2+6*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]^3+30*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]^2*s[3, 3]+6*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]-60*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]^2+114*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]*s[3, 3]+24*s[1, 1]*s[1, 2]*s[2, 1]*s[3, 3]^3-18*s[1, 1]*s[1, 2]*s[2, 2]^2*s[2, 3]*s[3, 1]+72*s[1, 1]*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 3]-108*s[1, 1]*s[1, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]-18*s[1, 1]*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]^2+54*s[1, 1]*s[1, 3]^2*s[2, 1]*s[3, 1]*s[3, 2]-24*s[1, 1]*s[1, 3]^2*s[2, 2]*s[3, 1]^2+30*s[1, 1]*s[1, 3]^2*s[3, 1]^2*s[3, 3]-18*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 2]+72*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]*s[3, 3]-108*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 2]^2-18*s[1, 1]*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]^2+24*s[1, 1]*s[1, 3]*s[2, 2]^3*s[3, 1]-60*s[1, 1]*s[1, 3]*s[2, 2]^2*s[3, 1]*s[3, 3]+114*s[1, 1]*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 2]+30*s[1, 1]*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]^2+6*s[1, 1]*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]+6*s[1, 1]*s[1, 3]*s[3, 1]*s[3, 3]^3+6*s[1, 1]*s[2, 2]^4*s[3, 3]-6*s[1, 1]*s[2, 2]^3*s[2, 3]*s[3, 2]-6*s[1, 1]*s[2, 2]^3*s[3, 3]^2+30*s[1, 1]*s[2, 2]^2*s[2, 3]*s[3, 2]*s[3, 3]-6*s[1, 1]*s[2, 2]^2*s[3, 3]^3-24*s[1, 1]*s[2, 2]*s[2, 3]^2*s[3, 2]^2+30*s[1, 1]*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]^2+6*s[1, 1]*s[2, 2]*s[3, 3]^4-24*s[1, 1]*s[2, 3]^2*s[3, 2]^2*s[3, 3]-6*s[1, 1]*s[2, 3]*s[3, 2]*s[3, 3]^3-12*s[1, 2]^3*s[2, 1]^3-36*s[1, 2]^2*s[1, 3]*s[2, 1]^2*s[3, 1]-3*s[1, 2]^2*s[2, 1]^2*s[2, 2]^2-24*s[1, 2]^2*s[2, 1]^2*s[2, 2]*s[3, 3]-36*s[1, 2]^2*s[2, 1]^2*s[2, 3]*s[3, 2]+24*s[1, 2]^2*s[2, 1]^2*s[3, 3]^2+54*s[1, 2]^2*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 1]-108*s[1, 2]^2*s[2, 1]*s[2, 3]*s[3, 1]*s[3, 3]+81*s[1, 2]^2*s[2, 3]^2*s[3, 1]^2-36*s[1, 2]*s[1, 3]^2*s[2, 1]*s[3, 1]^2+54*s[1, 2]*s[1, 3]*s[2, 1]^2*s[2, 2]*s[3, 2]-108*s[1, 2]*s[1, 3]*s[2, 1]^2*s[3, 2]*s[3, 3]-60*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 1]+114*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 1]*s[3, 3]+90*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 1]*s[3, 2]-60*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]*s[3, 3]^2-108*s[1, 2]*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]^2+54*s[1, 2]*s[1, 3]*s[2, 3]*s[3, 1]^2*s[3, 3]-6*s[1, 2]*s[2, 1]*s[2, 2]^3*s[3, 3]-6*s[1, 2]*s[2, 1]*s[2, 2]^2*s[2, 3]*s[3, 2]-6*s[1, 2]*s[2, 1]*s[2, 2]^2*s[3, 3]^2+6*s[1, 2]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]+24*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]^3-36*s[1, 2]*s[2, 1]*s[2, 3]^2*s[3, 2]^2-60*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]*s[3, 3]^2-12*s[1, 2]*s[2, 1]*s[3, 3]^4+12*s[1, 2]*s[2, 2]^3*s[2, 3]*s[3, 1]-18*s[1, 2]*s[2, 2]^2*s[2, 3]*s[3, 1]*s[3, 3]+54*s[1, 2]*s[2, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]-18*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 3]^2+54*s[1, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]*s[3, 3]+12*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]^3-12*s[1, 3]^3*s[3, 1]^3+81*s[1, 3]^2*s[2, 1]^2*s[3, 2]^2-108*s[1, 3]^2*s[2, 1]*s[2, 2]*s[3, 1]*s[3, 2]+54*s[1, 3]^2*s[2, 1]*s[3, 1]*s[3, 2]*s[3, 3]+24*s[1, 3]^2*s[2, 2]^2*s[3, 1]^2-24*s[1, 3]^2*s[2, 2]*s[3, 1]^2*s[3, 3]-36*s[1, 3]^2*s[2, 3]*s[3, 1]^2*s[3, 2]-3*s[1, 3]^2*s[3, 1]^2*s[3, 3]^2+12*s[1, 3]*s[2, 1]*s[2, 2]^3*s[3, 2]-18*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 2]*s[3, 3]+54*s[1, 3]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]^2-18*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]*s[3, 3]^2+54*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 2]^2*s[3, 3]+12*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]^3-12*s[1, 3]*s[2, 2]^4*s[3, 1]+24*s[1, 3]*s[2, 2]^3*s[3, 1]*s[3, 3]-60*s[1, 3]*s[2, 2]^2*s[2, 3]*s[3, 1]*s[3, 2]-6*s[1, 3]*s[2, 2]^2*s[3, 1]*s[3, 3]^2+6*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]-6*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]^3-36*s[1, 3]*s[2, 3]^2*s[3, 1]*s[3, 2]^2-6*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]^2-3*s[2, 2]^4*s[3, 3]^2+6*s[2, 2]^3*s[2, 3]*s[3, 2]*s[3, 3]+6*s[2, 2]^3*s[3, 3]^3-3*s[2, 2]^2*s[2, 3]^2*s[3, 2]^2-24*s[2, 2]^2*s[2, 3]*s[3, 2]*s[3, 3]^2-3*s[2, 2]^2*s[3, 3]^4+30*s[2, 2]*s[2, 3]^2*s[3, 2]^2*s[3, 3]+6*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]^3-12*s[2, 3]^3*s[3, 2]^3-3*s[2, 3]^2*s[3, 2]^2*s[3, 3]^2))^(1/3)+((1/3)*s[1, 1]*s[2, 2]+(1/3)*s[3, 3]*s[1, 1]-s[1, 2]*s[2, 1]-s[1, 3]*s[3, 1]+(1/3)*s[3, 3]*s[2, 2]-s[2, 3]*s[3, 2]-(1/3)*s[1, 1]^2-(1/3)*s[2, 2]^2-(1/3)*s[3, 3]^2)/(8*s[1, 1]^3-12*s[1, 1]^2*s[2, 2]-12*s[1, 1]^2*s[3, 3]+36*s[1, 1]*s[1, 2]*s[2, 1]+36*s[1, 1]*s[1, 3]*s[3, 1]-12*s[1, 1]*s[2, 2]^2+48*s[1, 1]*s[2, 2]*s[3, 3]-72*s[1, 1]*s[2, 3]*s[3, 2]-12*s[1, 1]*s[3, 3]^2+36*s[1, 2]*s[2, 1]*s[2, 2]-72*s[1, 2]*s[2, 1]*s[3, 3]+108*s[1, 2]*s[2, 3]*s[3, 1]+108*s[1, 3]*s[2, 1]*s[3, 2]-72*s[1, 3]*s[2, 2]*s[3, 1]+36*s[1, 3]*s[3, 1]*s[3, 3]+8*s[2, 2]^3-12*s[2, 2]^2*s[3, 3]+36*s[2, 2]*s[2, 3]*s[3, 2]-12*s[2, 2]*s[3, 3]^2+36*s[2, 3]*s[3, 2]*s[3, 3]+8*s[3, 3]^3+12*sqrt(-3*s[1, 1]^4*s[2, 2]^2+6*s[1, 1]^4*s[2, 2]*s[3, 3]-12*s[1, 1]^4*s[2, 3]*s[3, 2]-3*s[1, 1]^4*s[3, 3]^2+6*s[1, 1]^3*s[1, 2]*s[2, 1]*s[2, 2]-6*s[1, 1]^3*s[1, 2]*s[2, 1]*s[3, 3]+12*s[1, 1]^3*s[1, 2]*s[2, 3]*s[3, 1]+12*s[1, 1]^3*s[1, 3]*s[2, 1]*s[3, 2]-6*s[1, 1]^3*s[1, 3]*s[2, 2]*s[3, 1]+6*s[1, 1]^3*s[1, 3]*s[3, 1]*s[3, 3]+6*s[1, 1]^3*s[2, 2]^3-6*s[1, 1]^3*s[2, 2]^2*s[3, 3]+24*s[1, 1]^3*s[2, 2]*s[2, 3]*s[3, 2]-6*s[1, 1]^3*s[2, 2]*s[3, 3]^2+24*s[1, 1]^3*s[2, 3]*s[3, 2]*s[3, 3]+6*s[1, 1]^3*s[3, 3]^3-3*s[1, 1]^2*s[1, 2]^2*s[2, 1]^2-6*s[1, 1]^2*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]-24*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 2]^2+30*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]-60*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]-6*s[1, 1]^2*s[1, 2]*s[2, 1]*s[3, 3]^2-18*s[1, 1]^2*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]-18*s[1, 1]^2*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]-3*s[1, 1]^2*s[1, 3]^2*s[3, 1]^2-18*s[1, 1]^2*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]-18*s[1, 1]^2*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]-6*s[1, 1]^2*s[1, 3]*s[2, 2]^2*s[3, 1]+30*s[1, 1]^2*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]-60*s[1, 1]^2*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]-24*s[1, 1]^2*s[1, 3]*s[3, 1]*s[3, 3]^2-3*s[1, 1]^2*s[2, 2]^4-6*s[1, 1]^2*s[2, 2]^3*s[3, 3]-6*s[1, 1]^2*s[2, 2]^2*s[2, 3]*s[3, 2]+18*s[1, 1]^2*s[2, 2]^2*s[3, 3]^2-60*s[1, 1]^2*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]-6*s[1, 1]^2*s[2, 2]*s[3, 3]^3+24*s[1, 1]^2*s[2, 3]^2*s[3, 2]^2-6*s[1, 1]^2*s[2, 3]*s[3, 2]*s[3, 3]^2-3*s[1, 1]^2*s[3, 3]^4+30*s[1, 1]*s[1, 2]^2*s[2, 1]^2*s[2, 2]-24*s[1, 1]*s[1, 2]^2*s[2, 1]^2*s[3, 3]+54*s[1, 1]*s[1, 2]^2*s[2, 1]*s[2, 3]*s[3, 1]+54*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]^2*s[3, 2]+6*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 1]+6*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]*s[3, 3]+54*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 3]*s[3, 1]^2+6*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]^3+30*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]^2*s[3, 3]+6*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]-60*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]^2+114*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]*s[3, 3]+24*s[1, 1]*s[1, 2]*s[2, 1]*s[3, 3]^3-18*s[1, 1]*s[1, 2]*s[2, 2]^2*s[2, 3]*s[3, 1]+72*s[1, 1]*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 3]-108*s[1, 1]*s[1, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]-18*s[1, 1]*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]^2+54*s[1, 1]*s[1, 3]^2*s[2, 1]*s[3, 1]*s[3, 2]-24*s[1, 1]*s[1, 3]^2*s[2, 2]*s[3, 1]^2+30*s[1, 1]*s[1, 3]^2*s[3, 1]^2*s[3, 3]-18*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 2]+72*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]*s[3, 3]-108*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 2]^2-18*s[1, 1]*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]^2+24*s[1, 1]*s[1, 3]*s[2, 2]^3*s[3, 1]-60*s[1, 1]*s[1, 3]*s[2, 2]^2*s[3, 1]*s[3, 3]+114*s[1, 1]*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 2]+30*s[1, 1]*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]^2+6*s[1, 1]*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]+6*s[1, 1]*s[1, 3]*s[3, 1]*s[3, 3]^3+6*s[1, 1]*s[2, 2]^4*s[3, 3]-6*s[1, 1]*s[2, 2]^3*s[2, 3]*s[3, 2]-6*s[1, 1]*s[2, 2]^3*s[3, 3]^2+30*s[1, 1]*s[2, 2]^2*s[2, 3]*s[3, 2]*s[3, 3]-6*s[1, 1]*s[2, 2]^2*s[3, 3]^3-24*s[1, 1]*s[2, 2]*s[2, 3]^2*s[3, 2]^2+30*s[1, 1]*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]^2+6*s[1, 1]*s[2, 2]*s[3, 3]^4-24*s[1, 1]*s[2, 3]^2*s[3, 2]^2*s[3, 3]-6*s[1, 1]*s[2, 3]*s[3, 2]*s[3, 3]^3-12*s[1, 2]^3*s[2, 1]^3-36*s[1, 2]^2*s[1, 3]*s[2, 1]^2*s[3, 1]-3*s[1, 2]^2*s[2, 1]^2*s[2, 2]^2-24*s[1, 2]^2*s[2, 1]^2*s[2, 2]*s[3, 3]-36*s[1, 2]^2*s[2, 1]^2*s[2, 3]*s[3, 2]+24*s[1, 2]^2*s[2, 1]^2*s[3, 3]^2+54*s[1, 2]^2*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 1]-108*s[1, 2]^2*s[2, 1]*s[2, 3]*s[3, 1]*s[3, 3]+81*s[1, 2]^2*s[2, 3]^2*s[3, 1]^2-36*s[1, 2]*s[1, 3]^2*s[2, 1]*s[3, 1]^2+54*s[1, 2]*s[1, 3]*s[2, 1]^2*s[2, 2]*s[3, 2]-108*s[1, 2]*s[1, 3]*s[2, 1]^2*s[3, 2]*s[3, 3]-60*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 1]+114*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 1]*s[3, 3]+90*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 1]*s[3, 2]-60*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]*s[3, 3]^2-108*s[1, 2]*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]^2+54*s[1, 2]*s[1, 3]*s[2, 3]*s[3, 1]^2*s[3, 3]-6*s[1, 2]*s[2, 1]*s[2, 2]^3*s[3, 3]-6*s[1, 2]*s[2, 1]*s[2, 2]^2*s[2, 3]*s[3, 2]-6*s[1, 2]*s[2, 1]*s[2, 2]^2*s[3, 3]^2+6*s[1, 2]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]+24*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]^3-36*s[1, 2]*s[2, 1]*s[2, 3]^2*s[3, 2]^2-60*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]*s[3, 3]^2-12*s[1, 2]*s[2, 1]*s[3, 3]^4+12*s[1, 2]*s[2, 2]^3*s[2, 3]*s[3, 1]-18*s[1, 2]*s[2, 2]^2*s[2, 3]*s[3, 1]*s[3, 3]+54*s[1, 2]*s[2, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]-18*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 3]^2+54*s[1, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]*s[3, 3]+12*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]^3-12*s[1, 3]^3*s[3, 1]^3+81*s[1, 3]^2*s[2, 1]^2*s[3, 2]^2-108*s[1, 3]^2*s[2, 1]*s[2, 2]*s[3, 1]*s[3, 2]+54*s[1, 3]^2*s[2, 1]*s[3, 1]*s[3, 2]*s[3, 3]+24*s[1, 3]^2*s[2, 2]^2*s[3, 1]^2-24*s[1, 3]^2*s[2, 2]*s[3, 1]^2*s[3, 3]-36*s[1, 3]^2*s[2, 3]*s[3, 1]^2*s[3, 2]-3*s[1, 3]^2*s[3, 1]^2*s[3, 3]^2+12*s[1, 3]*s[2, 1]*s[2, 2]^3*s[3, 2]-18*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 2]*s[3, 3]+54*s[1, 3]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]^2-18*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]*s[3, 3]^2+54*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 2]^2*s[3, 3]+12*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]^3-12*s[1, 3]*s[2, 2]^4*s[3, 1]+24*s[1, 3]*s[2, 2]^3*s[3, 1]*s[3, 3]-60*s[1, 3]*s[2, 2]^2*s[2, 3]*s[3, 1]*s[3, 2]-6*s[1, 3]*s[2, 2]^2*s[3, 1]*s[3, 3]^2+6*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]-6*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]^3-36*s[1, 3]*s[2, 3]^2*s[3, 1]*s[3, 2]^2-6*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]^2-3*s[2, 2]^4*s[3, 3]^2+6*s[2, 2]^3*s[2, 3]*s[3, 2]*s[3, 3]+6*s[2, 2]^3*s[3, 3]^3-3*s[2, 2]^2*s[2, 3]^2*s[3, 2]^2-24*s[2, 2]^2*s[2, 3]*s[3, 2]*s[3, 3]^2-3*s[2, 2]^2*s[3, 3]^4+30*s[2, 2]*s[2, 3]^2*s[3, 2]^2*s[3, 3]+6*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]^3-12*s[2, 3]^3*s[3, 2]^3-3*s[2, 3]^2*s[3, 2]^2*s[3, 3]^2))^(1/3)+(1/3)*s[3, 3]+(1/3)*s[2, 2]+(1/3)*s[1, 1]+((1/2)*I)*sqrt(3)*((1/6)*(8*s[1, 1]^3-12*s[1, 1]^2*s[2, 2]-12*s[1, 1]^2*s[3, 3]+36*s[1, 1]*s[1, 2]*s[2, 1]+36*s[1, 1]*s[1, 3]*s[3, 1]-12*s[1, 1]*s[2, 2]^2+48*s[1, 1]*s[2, 2]*s[3, 3]-72*s[1, 1]*s[2, 3]*s[3, 2]-12*s[1, 1]*s[3, 3]^2+36*s[1, 2]*s[2, 1]*s[2, 2]-72*s[1, 2]*s[2, 1]*s[3, 3]+108*s[1, 2]*s[2, 3]*s[3, 1]+108*s[1, 3]*s[2, 1]*s[3, 2]-72*s[1, 3]*s[2, 2]*s[3, 1]+36*s[1, 3]*s[3, 1]*s[3, 3]+8*s[2, 2]^3-12*s[2, 2]^2*s[3, 3]+36*s[2, 2]*s[2, 3]*s[3, 2]-12*s[2, 2]*s[3, 3]^2+36*s[2, 3]*s[3, 2]*s[3, 3]+8*s[3, 3]^3+12*sqrt(-3*s[1, 1]^4*s[2, 2]^2+6*s[1, 1]^4*s[2, 2]*s[3, 3]-12*s[1, 1]^4*s[2, 3]*s[3, 2]-3*s[1, 1]^4*s[3, 3]^2+6*s[1, 1]^3*s[1, 2]*s[2, 1]*s[2, 2]-6*s[1, 1]^3*s[1, 2]*s[2, 1]*s[3, 3]+12*s[1, 1]^3*s[1, 2]*s[2, 3]*s[3, 1]+12*s[1, 1]^3*s[1, 3]*s[2, 1]*s[3, 2]-6*s[1, 1]^3*s[1, 3]*s[2, 2]*s[3, 1]+6*s[1, 1]^3*s[1, 3]*s[3, 1]*s[3, 3]+6*s[1, 1]^3*s[2, 2]^3-6*s[1, 1]^3*s[2, 2]^2*s[3, 3]+24*s[1, 1]^3*s[2, 2]*s[2, 3]*s[3, 2]-6*s[1, 1]^3*s[2, 2]*s[3, 3]^2+24*s[1, 1]^3*s[2, 3]*s[3, 2]*s[3, 3]+6*s[1, 1]^3*s[3, 3]^3-3*s[1, 1]^2*s[1, 2]^2*s[2, 1]^2-6*s[1, 1]^2*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]-24*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 2]^2+30*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]-60*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]-6*s[1, 1]^2*s[1, 2]*s[2, 1]*s[3, 3]^2-18*s[1, 1]^2*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]-18*s[1, 1]^2*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]-3*s[1, 1]^2*s[1, 3]^2*s[3, 1]^2-18*s[1, 1]^2*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]-18*s[1, 1]^2*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]-6*s[1, 1]^2*s[1, 3]*s[2, 2]^2*s[3, 1]+30*s[1, 1]^2*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]-60*s[1, 1]^2*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]-24*s[1, 1]^2*s[1, 3]*s[3, 1]*s[3, 3]^2-3*s[1, 1]^2*s[2, 2]^4-6*s[1, 1]^2*s[2, 2]^3*s[3, 3]-6*s[1, 1]^2*s[2, 2]^2*s[2, 3]*s[3, 2]+18*s[1, 1]^2*s[2, 2]^2*s[3, 3]^2-60*s[1, 1]^2*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]-6*s[1, 1]^2*s[2, 2]*s[3, 3]^3+24*s[1, 1]^2*s[2, 3]^2*s[3, 2]^2-6*s[1, 1]^2*s[2, 3]*s[3, 2]*s[3, 3]^2-3*s[1, 1]^2*s[3, 3]^4+30*s[1, 1]*s[1, 2]^2*s[2, 1]^2*s[2, 2]-24*s[1, 1]*s[1, 2]^2*s[2, 1]^2*s[3, 3]+54*s[1, 1]*s[1, 2]^2*s[2, 1]*s[2, 3]*s[3, 1]+54*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]^2*s[3, 2]+6*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 1]+6*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]*s[3, 3]+54*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 3]*s[3, 1]^2+6*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]^3+30*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]^2*s[3, 3]+6*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]-60*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]^2+114*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]*s[3, 3]+24*s[1, 1]*s[1, 2]*s[2, 1]*s[3, 3]^3-18*s[1, 1]*s[1, 2]*s[2, 2]^2*s[2, 3]*s[3, 1]+72*s[1, 1]*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 3]-108*s[1, 1]*s[1, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]-18*s[1, 1]*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]^2+54*s[1, 1]*s[1, 3]^2*s[2, 1]*s[3, 1]*s[3, 2]-24*s[1, 1]*s[1, 3]^2*s[2, 2]*s[3, 1]^2+30*s[1, 1]*s[1, 3]^2*s[3, 1]^2*s[3, 3]-18*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 2]+72*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]*s[3, 3]-108*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 2]^2-18*s[1, 1]*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]^2+24*s[1, 1]*s[1, 3]*s[2, 2]^3*s[3, 1]-60*s[1, 1]*s[1, 3]*s[2, 2]^2*s[3, 1]*s[3, 3]+114*s[1, 1]*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 2]+30*s[1, 1]*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]^2+6*s[1, 1]*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]+6*s[1, 1]*s[1, 3]*s[3, 1]*s[3, 3]^3+6*s[1, 1]*s[2, 2]^4*s[3, 3]-6*s[1, 1]*s[2, 2]^3*s[2, 3]*s[3, 2]-6*s[1, 1]*s[2, 2]^3*s[3, 3]^2+30*s[1, 1]*s[2, 2]^2*s[2, 3]*s[3, 2]*s[3, 3]-6*s[1, 1]*s[2, 2]^2*s[3, 3]^3-24*s[1, 1]*s[2, 2]*s[2, 3]^2*s[3, 2]^2+30*s[1, 1]*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]^2+6*s[1, 1]*s[2, 2]*s[3, 3]^4-24*s[1, 1]*s[2, 3]^2*s[3, 2]^2*s[3, 3]-6*s[1, 1]*s[2, 3]*s[3, 2]*s[3, 3]^3-12*s[1, 2]^3*s[2, 1]^3-36*s[1, 2]^2*s[1, 3]*s[2, 1]^2*s[3, 1]-3*s[1, 2]^2*s[2, 1]^2*s[2, 2]^2-24*s[1, 2]^2*s[2, 1]^2*s[2, 2]*s[3, 3]-36*s[1, 2]^2*s[2, 1]^2*s[2, 3]*s[3, 2]+24*s[1, 2]^2*s[2, 1]^2*s[3, 3]^2+54*s[1, 2]^2*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 1]-108*s[1, 2]^2*s[2, 1]*s[2, 3]*s[3, 1]*s[3, 3]+81*s[1, 2]^2*s[2, 3]^2*s[3, 1]^2-36*s[1, 2]*s[1, 3]^2*s[2, 1]*s[3, 1]^2+54*s[1, 2]*s[1, 3]*s[2, 1]^2*s[2, 2]*s[3, 2]-108*s[1, 2]*s[1, 3]*s[2, 1]^2*s[3, 2]*s[3, 3]-60*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 1]+114*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 1]*s[3, 3]+90*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 1]*s[3, 2]-60*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]*s[3, 3]^2-108*s[1, 2]*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]^2+54*s[1, 2]*s[1, 3]*s[2, 3]*s[3, 1]^2*s[3, 3]-6*s[1, 2]*s[2, 1]*s[2, 2]^3*s[3, 3]-6*s[1, 2]*s[2, 1]*s[2, 2]^2*s[2, 3]*s[3, 2]-6*s[1, 2]*s[2, 1]*s[2, 2]^2*s[3, 3]^2+6*s[1, 2]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]+24*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]^3-36*s[1, 2]*s[2, 1]*s[2, 3]^2*s[3, 2]^2-60*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]*s[3, 3]^2-12*s[1, 2]*s[2, 1]*s[3, 3]^4+12*s[1, 2]*s[2, 2]^3*s[2, 3]*s[3, 1]-18*s[1, 2]*s[2, 2]^2*s[2, 3]*s[3, 1]*s[3, 3]+54*s[1, 2]*s[2, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]-18*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 3]^2+54*s[1, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]*s[3, 3]+12*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]^3-12*s[1, 3]^3*s[3, 1]^3+81*s[1, 3]^2*s[2, 1]^2*s[3, 2]^2-108*s[1, 3]^2*s[2, 1]*s[2, 2]*s[3, 1]*s[3, 2]+54*s[1, 3]^2*s[2, 1]*s[3, 1]*s[3, 2]*s[3, 3]+24*s[1, 3]^2*s[2, 2]^2*s[3, 1]^2-24*s[1, 3]^2*s[2, 2]*s[3, 1]^2*s[3, 3]-36*s[1, 3]^2*s[2, 3]*s[3, 1]^2*s[3, 2]-3*s[1, 3]^2*s[3, 1]^2*s[3, 3]^2+12*s[1, 3]*s[2, 1]*s[2, 2]^3*s[3, 2]-18*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 2]*s[3, 3]+54*s[1, 3]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]^2-18*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]*s[3, 3]^2+54*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 2]^2*s[3, 3]+12*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]^3-12*s[1, 3]*s[2, 2]^4*s[3, 1]+24*s[1, 3]*s[2, 2]^3*s[3, 1]*s[3, 3]-60*s[1, 3]*s[2, 2]^2*s[2, 3]*s[3, 1]*s[3, 2]-6*s[1, 3]*s[2, 2]^2*s[3, 1]*s[3, 3]^2+6*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]-6*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]^3-36*s[1, 3]*s[2, 3]^2*s[3, 1]*s[3, 2]^2-6*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]^2-3*s[2, 2]^4*s[3, 3]^2+6*s[2, 2]^3*s[2, 3]*s[3, 2]*s[3, 3]+6*s[2, 2]^3*s[3, 3]^3-3*s[2, 2]^2*s[2, 3]^2*s[3, 2]^2-24*s[2, 2]^2*s[2, 3]*s[3, 2]*s[3, 3]^2-3*s[2, 2]^2*s[3, 3]^4+30*s[2, 2]*s[2, 3]^2*s[3, 2]^2*s[3, 3]+6*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]^3-12*s[2, 3]^3*s[3, 2]^3-3*s[2, 3]^2*s[3, 2]^2*s[3, 3]^2))^(1/3)+((2/3)*s[1, 1]*s[2, 2]+(2/3)*s[3, 3]*s[1, 1]-2*s[1, 2]*s[2, 1]-2*s[1, 3]*s[3, 1]+(2/3)*s[3, 3]*s[2, 2]-2*s[2, 3]*s[3, 2]-(2/3)*s[1, 1]^2-(2/3)*s[2, 2]^2-(2/3)*s[3, 3]^2)/(8*s[1, 1]^3-12*s[1, 1]^2*s[2, 2]-12*s[1, 1]^2*s[3, 3]+36*s[1, 1]*s[1, 2]*s[2, 1]+36*s[1, 1]*s[1, 3]*s[3, 1]-12*s[1, 1]*s[2, 2]^2+48*s[1, 1]*s[2, 2]*s[3, 3]-72*s[1, 1]*s[2, 3]*s[3, 2]-12*s[1, 1]*s[3, 3]^2+36*s[1, 2]*s[2, 1]*s[2, 2]-72*s[1, 2]*s[2, 1]*s[3, 3]+108*s[1, 2]*s[2, 3]*s[3, 1]+108*s[1, 3]*s[2, 1]*s[3, 2]-72*s[1, 3]*s[2, 2]*s[3, 1]+36*s[1, 3]*s[3, 1]*s[3, 3]+8*s[2, 2]^3-12*s[2, 2]^2*s[3, 3]+36*s[2, 2]*s[2, 3]*s[3, 2]-12*s[2, 2]*s[3, 3]^2+36*s[2, 3]*s[3, 2]*s[3, 3]+8*s[3, 3]^3+12*sqrt(-3*s[1, 1]^4*s[2, 2]^2+6*s[1, 1]^4*s[2, 2]*s[3, 3]-12*s[1, 1]^4*s[2, 3]*s[3, 2]-3*s[1, 1]^4*s[3, 3]^2+6*s[1, 1]^3*s[1, 2]*s[2, 1]*s[2, 2]-6*s[1, 1]^3*s[1, 2]*s[2, 1]*s[3, 3]+12*s[1, 1]^3*s[1, 2]*s[2, 3]*s[3, 1]+12*s[1, 1]^3*s[1, 3]*s[2, 1]*s[3, 2]-6*s[1, 1]^3*s[1, 3]*s[2, 2]*s[3, 1]+6*s[1, 1]^3*s[1, 3]*s[3, 1]*s[3, 3]+6*s[1, 1]^3*s[2, 2]^3-6*s[1, 1]^3*s[2, 2]^2*s[3, 3]+24*s[1, 1]^3*s[2, 2]*s[2, 3]*s[3, 2]-6*s[1, 1]^3*s[2, 2]*s[3, 3]^2+24*s[1, 1]^3*s[2, 3]*s[3, 2]*s[3, 3]+6*s[1, 1]^3*s[3, 3]^3-3*s[1, 1]^2*s[1, 2]^2*s[2, 1]^2-6*s[1, 1]^2*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]-24*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 2]^2+30*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]-60*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]-6*s[1, 1]^2*s[1, 2]*s[2, 1]*s[3, 3]^2-18*s[1, 1]^2*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]-18*s[1, 1]^2*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]-3*s[1, 1]^2*s[1, 3]^2*s[3, 1]^2-18*s[1, 1]^2*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]-18*s[1, 1]^2*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]-6*s[1, 1]^2*s[1, 3]*s[2, 2]^2*s[3, 1]+30*s[1, 1]^2*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]-60*s[1, 1]^2*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]-24*s[1, 1]^2*s[1, 3]*s[3, 1]*s[3, 3]^2-3*s[1, 1]^2*s[2, 2]^4-6*s[1, 1]^2*s[2, 2]^3*s[3, 3]-6*s[1, 1]^2*s[2, 2]^2*s[2, 3]*s[3, 2]+18*s[1, 1]^2*s[2, 2]^2*s[3, 3]^2-60*s[1, 1]^2*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]-6*s[1, 1]^2*s[2, 2]*s[3, 3]^3+24*s[1, 1]^2*s[2, 3]^2*s[3, 2]^2-6*s[1, 1]^2*s[2, 3]*s[3, 2]*s[3, 3]^2-3*s[1, 1]^2*s[3, 3]^4+30*s[1, 1]*s[1, 2]^2*s[2, 1]^2*s[2, 2]-24*s[1, 1]*s[1, 2]^2*s[2, 1]^2*s[3, 3]+54*s[1, 1]*s[1, 2]^2*s[2, 1]*s[2, 3]*s[3, 1]+54*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]^2*s[3, 2]+6*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 1]+6*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]*s[3, 3]+54*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 3]*s[3, 1]^2+6*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]^3+30*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]^2*s[3, 3]+6*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]-60*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]^2+114*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]*s[3, 3]+24*s[1, 1]*s[1, 2]*s[2, 1]*s[3, 3]^3-18*s[1, 1]*s[1, 2]*s[2, 2]^2*s[2, 3]*s[3, 1]+72*s[1, 1]*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 3]-108*s[1, 1]*s[1, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]-18*s[1, 1]*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]^2+54*s[1, 1]*s[1, 3]^2*s[2, 1]*s[3, 1]*s[3, 2]-24*s[1, 1]*s[1, 3]^2*s[2, 2]*s[3, 1]^2+30*s[1, 1]*s[1, 3]^2*s[3, 1]^2*s[3, 3]-18*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 2]+72*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]*s[3, 3]-108*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 2]^2-18*s[1, 1]*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]^2+24*s[1, 1]*s[1, 3]*s[2, 2]^3*s[3, 1]-60*s[1, 1]*s[1, 3]*s[2, 2]^2*s[3, 1]*s[3, 3]+114*s[1, 1]*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 2]+30*s[1, 1]*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]^2+6*s[1, 1]*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]+6*s[1, 1]*s[1, 3]*s[3, 1]*s[3, 3]^3+6*s[1, 1]*s[2, 2]^4*s[3, 3]-6*s[1, 1]*s[2, 2]^3*s[2, 3]*s[3, 2]-6*s[1, 1]*s[2, 2]^3*s[3, 3]^2+30*s[1, 1]*s[2, 2]^2*s[2, 3]*s[3, 2]*s[3, 3]-6*s[1, 1]*s[2, 2]^2*s[3, 3]^3-24*s[1, 1]*s[2, 2]*s[2, 3]^2*s[3, 2]^2+30*s[1, 1]*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]^2+6*s[1, 1]*s[2, 2]*s[3, 3]^4-24*s[1, 1]*s[2, 3]^2*s[3, 2]^2*s[3, 3]-6*s[1, 1]*s[2, 3]*s[3, 2]*s[3, 3]^3-12*s[1, 2]^3*s[2, 1]^3-36*s[1, 2]^2*s[1, 3]*s[2, 1]^2*s[3, 1]-3*s[1, 2]^2*s[2, 1]^2*s[2, 2]^2-24*s[1, 2]^2*s[2, 1]^2*s[2, 2]*s[3, 3]-36*s[1, 2]^2*s[2, 1]^2*s[2, 3]*s[3, 2]+24*s[1, 2]^2*s[2, 1]^2*s[3, 3]^2+54*s[1, 2]^2*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 1]-108*s[1, 2]^2*s[2, 1]*s[2, 3]*s[3, 1]*s[3, 3]+81*s[1, 2]^2*s[2, 3]^2*s[3, 1]^2-36*s[1, 2]*s[1, 3]^2*s[2, 1]*s[3, 1]^2+54*s[1, 2]*s[1, 3]*s[2, 1]^2*s[2, 2]*s[3, 2]-108*s[1, 2]*s[1, 3]*s[2, 1]^2*s[3, 2]*s[3, 3]-60*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 1]+114*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 1]*s[3, 3]+90*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 1]*s[3, 2]-60*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]*s[3, 3]^2-108*s[1, 2]*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]^2+54*s[1, 2]*s[1, 3]*s[2, 3]*s[3, 1]^2*s[3, 3]-6*s[1, 2]*s[2, 1]*s[2, 2]^3*s[3, 3]-6*s[1, 2]*s[2, 1]*s[2, 2]^2*s[2, 3]*s[3, 2]-6*s[1, 2]*s[2, 1]*s[2, 2]^2*s[3, 3]^2+6*s[1, 2]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]+24*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]^3-36*s[1, 2]*s[2, 1]*s[2, 3]^2*s[3, 2]^2-60*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]*s[3, 3]^2-12*s[1, 2]*s[2, 1]*s[3, 3]^4+12*s[1, 2]*s[2, 2]^3*s[2, 3]*s[3, 1]-18*s[1, 2]*s[2, 2]^2*s[2, 3]*s[3, 1]*s[3, 3]+54*s[1, 2]*s[2, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]-18*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 3]^2+54*s[1, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]*s[3, 3]+12*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]^3-12*s[1, 3]^3*s[3, 1]^3+81*s[1, 3]^2*s[2, 1]^2*s[3, 2]^2-108*s[1, 3]^2*s[2, 1]*s[2, 2]*s[3, 1]*s[3, 2]+54*s[1, 3]^2*s[2, 1]*s[3, 1]*s[3, 2]*s[3, 3]+24*s[1, 3]^2*s[2, 2]^2*s[3, 1]^2-24*s[1, 3]^2*s[2, 2]*s[3, 1]^2*s[3, 3]-36*s[1, 3]^2*s[2, 3]*s[3, 1]^2*s[3, 2]-3*s[1, 3]^2*s[3, 1]^2*s[3, 3]^2+12*s[1, 3]*s[2, 1]*s[2, 2]^3*s[3, 2]-18*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 2]*s[3, 3]+54*s[1, 3]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]^2-18*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]*s[3, 3]^2+54*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 2]^2*s[3, 3]+12*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]^3-12*s[1, 3]*s[2, 2]^4*s[3, 1]+24*s[1, 3]*s[2, 2]^3*s[3, 1]*s[3, 3]-60*s[1, 3]*s[2, 2]^2*s[2, 3]*s[3, 1]*s[3, 2]-6*s[1, 3]*s[2, 2]^2*s[3, 1]*s[3, 3]^2+6*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]-6*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]^3-36*s[1, 3]*s[2, 3]^2*s[3, 1]*s[3, 2]^2-6*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]^2-3*s[2, 2]^4*s[3, 3]^2+6*s[2, 2]^3*s[2, 3]*s[3, 2]*s[3, 3]+6*s[2, 2]^3*s[3, 3]^3-3*s[2, 2]^2*s[2, 3]^2*s[3, 2]^2-24*s[2, 2]^2*s[2, 3]*s[3, 2]*s[3, 3]^2-3*s[2, 2]^2*s[3, 3]^4+30*s[2, 2]*s[2, 3]^2*s[3, 2]^2*s[3, 3]+6*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]^3-12*s[2, 3]^3*s[3, 2]^3-3*s[2, 3]^2*s[3, 2]^2*s[3, 3]^2))^(1/3)), (3) = -(1/12)*(8*s[1, 1]^3-12*s[1, 1]^2*s[2, 2]-12*s[1, 1]^2*s[3, 3]+36*s[1, 1]*s[1, 2]*s[2, 1]+36*s[1, 1]*s[1, 3]*s[3, 1]-12*s[1, 1]*s[2, 2]^2+48*s[1, 1]*s[2, 2]*s[3, 3]-72*s[1, 1]*s[2, 3]*s[3, 2]-12*s[1, 1]*s[3, 3]^2+36*s[1, 2]*s[2, 1]*s[2, 2]-72*s[1, 2]*s[2, 1]*s[3, 3]+108*s[1, 2]*s[2, 3]*s[3, 1]+108*s[1, 3]*s[2, 1]*s[3, 2]-72*s[1, 3]*s[2, 2]*s[3, 1]+36*s[1, 3]*s[3, 1]*s[3, 3]+8*s[2, 2]^3-12*s[2, 2]^2*s[3, 3]+36*s[2, 2]*s[2, 3]*s[3, 2]-12*s[2, 2]*s[3, 3]^2+36*s[2, 3]*s[3, 2]*s[3, 3]+8*s[3, 3]^3+12*sqrt(-3*s[1, 1]^4*s[2, 2]^2+6*s[1, 1]^4*s[2, 2]*s[3, 3]-12*s[1, 1]^4*s[2, 3]*s[3, 2]-3*s[1, 1]^4*s[3, 3]^2+6*s[1, 1]^3*s[1, 2]*s[2, 1]*s[2, 2]-6*s[1, 1]^3*s[1, 2]*s[2, 1]*s[3, 3]+12*s[1, 1]^3*s[1, 2]*s[2, 3]*s[3, 1]+12*s[1, 1]^3*s[1, 3]*s[2, 1]*s[3, 2]-6*s[1, 1]^3*s[1, 3]*s[2, 2]*s[3, 1]+6*s[1, 1]^3*s[1, 3]*s[3, 1]*s[3, 3]+6*s[1, 1]^3*s[2, 2]^3-6*s[1, 1]^3*s[2, 2]^2*s[3, 3]+24*s[1, 1]^3*s[2, 2]*s[2, 3]*s[3, 2]-6*s[1, 1]^3*s[2, 2]*s[3, 3]^2+24*s[1, 1]^3*s[2, 3]*s[3, 2]*s[3, 3]+6*s[1, 1]^3*s[3, 3]^3-3*s[1, 1]^2*s[1, 2]^2*s[2, 1]^2-6*s[1, 1]^2*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]-24*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 2]^2+30*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]-60*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]-6*s[1, 1]^2*s[1, 2]*s[2, 1]*s[3, 3]^2-18*s[1, 1]^2*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]-18*s[1, 1]^2*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]-3*s[1, 1]^2*s[1, 3]^2*s[3, 1]^2-18*s[1, 1]^2*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]-18*s[1, 1]^2*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]-6*s[1, 1]^2*s[1, 3]*s[2, 2]^2*s[3, 1]+30*s[1, 1]^2*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]-60*s[1, 1]^2*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]-24*s[1, 1]^2*s[1, 3]*s[3, 1]*s[3, 3]^2-3*s[1, 1]^2*s[2, 2]^4-6*s[1, 1]^2*s[2, 2]^3*s[3, 3]-6*s[1, 1]^2*s[2, 2]^2*s[2, 3]*s[3, 2]+18*s[1, 1]^2*s[2, 2]^2*s[3, 3]^2-60*s[1, 1]^2*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]-6*s[1, 1]^2*s[2, 2]*s[3, 3]^3+24*s[1, 1]^2*s[2, 3]^2*s[3, 2]^2-6*s[1, 1]^2*s[2, 3]*s[3, 2]*s[3, 3]^2-3*s[1, 1]^2*s[3, 3]^4+30*s[1, 1]*s[1, 2]^2*s[2, 1]^2*s[2, 2]-24*s[1, 1]*s[1, 2]^2*s[2, 1]^2*s[3, 3]+54*s[1, 1]*s[1, 2]^2*s[2, 1]*s[2, 3]*s[3, 1]+54*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]^2*s[3, 2]+6*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 1]+6*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]*s[3, 3]+54*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 3]*s[3, 1]^2+6*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]^3+30*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]^2*s[3, 3]+6*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]-60*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]^2+114*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]*s[3, 3]+24*s[1, 1]*s[1, 2]*s[2, 1]*s[3, 3]^3-18*s[1, 1]*s[1, 2]*s[2, 2]^2*s[2, 3]*s[3, 1]+72*s[1, 1]*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 3]-108*s[1, 1]*s[1, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]-18*s[1, 1]*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]^2+54*s[1, 1]*s[1, 3]^2*s[2, 1]*s[3, 1]*s[3, 2]-24*s[1, 1]*s[1, 3]^2*s[2, 2]*s[3, 1]^2+30*s[1, 1]*s[1, 3]^2*s[3, 1]^2*s[3, 3]-18*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 2]+72*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]*s[3, 3]-108*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 2]^2-18*s[1, 1]*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]^2+24*s[1, 1]*s[1, 3]*s[2, 2]^3*s[3, 1]-60*s[1, 1]*s[1, 3]*s[2, 2]^2*s[3, 1]*s[3, 3]+114*s[1, 1]*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 2]+30*s[1, 1]*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]^2+6*s[1, 1]*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]+6*s[1, 1]*s[1, 3]*s[3, 1]*s[3, 3]^3+6*s[1, 1]*s[2, 2]^4*s[3, 3]-6*s[1, 1]*s[2, 2]^3*s[2, 3]*s[3, 2]-6*s[1, 1]*s[2, 2]^3*s[3, 3]^2+30*s[1, 1]*s[2, 2]^2*s[2, 3]*s[3, 2]*s[3, 3]-6*s[1, 1]*s[2, 2]^2*s[3, 3]^3-24*s[1, 1]*s[2, 2]*s[2, 3]^2*s[3, 2]^2+30*s[1, 1]*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]^2+6*s[1, 1]*s[2, 2]*s[3, 3]^4-24*s[1, 1]*s[2, 3]^2*s[3, 2]^2*s[3, 3]-6*s[1, 1]*s[2, 3]*s[3, 2]*s[3, 3]^3-12*s[1, 2]^3*s[2, 1]^3-36*s[1, 2]^2*s[1, 3]*s[2, 1]^2*s[3, 1]-3*s[1, 2]^2*s[2, 1]^2*s[2, 2]^2-24*s[1, 2]^2*s[2, 1]^2*s[2, 2]*s[3, 3]-36*s[1, 2]^2*s[2, 1]^2*s[2, 3]*s[3, 2]+24*s[1, 2]^2*s[2, 1]^2*s[3, 3]^2+54*s[1, 2]^2*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 1]-108*s[1, 2]^2*s[2, 1]*s[2, 3]*s[3, 1]*s[3, 3]+81*s[1, 2]^2*s[2, 3]^2*s[3, 1]^2-36*s[1, 2]*s[1, 3]^2*s[2, 1]*s[3, 1]^2+54*s[1, 2]*s[1, 3]*s[2, 1]^2*s[2, 2]*s[3, 2]-108*s[1, 2]*s[1, 3]*s[2, 1]^2*s[3, 2]*s[3, 3]-60*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 1]+114*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 1]*s[3, 3]+90*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 1]*s[3, 2]-60*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]*s[3, 3]^2-108*s[1, 2]*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]^2+54*s[1, 2]*s[1, 3]*s[2, 3]*s[3, 1]^2*s[3, 3]-6*s[1, 2]*s[2, 1]*s[2, 2]^3*s[3, 3]-6*s[1, 2]*s[2, 1]*s[2, 2]^2*s[2, 3]*s[3, 2]-6*s[1, 2]*s[2, 1]*s[2, 2]^2*s[3, 3]^2+6*s[1, 2]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]+24*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]^3-36*s[1, 2]*s[2, 1]*s[2, 3]^2*s[3, 2]^2-60*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]*s[3, 3]^2-12*s[1, 2]*s[2, 1]*s[3, 3]^4+12*s[1, 2]*s[2, 2]^3*s[2, 3]*s[3, 1]-18*s[1, 2]*s[2, 2]^2*s[2, 3]*s[3, 1]*s[3, 3]+54*s[1, 2]*s[2, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]-18*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 3]^2+54*s[1, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]*s[3, 3]+12*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]^3-12*s[1, 3]^3*s[3, 1]^3+81*s[1, 3]^2*s[2, 1]^2*s[3, 2]^2-108*s[1, 3]^2*s[2, 1]*s[2, 2]*s[3, 1]*s[3, 2]+54*s[1, 3]^2*s[2, 1]*s[3, 1]*s[3, 2]*s[3, 3]+24*s[1, 3]^2*s[2, 2]^2*s[3, 1]^2-24*s[1, 3]^2*s[2, 2]*s[3, 1]^2*s[3, 3]-36*s[1, 3]^2*s[2, 3]*s[3, 1]^2*s[3, 2]-3*s[1, 3]^2*s[3, 1]^2*s[3, 3]^2+12*s[1, 3]*s[2, 1]*s[2, 2]^3*s[3, 2]-18*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 2]*s[3, 3]+54*s[1, 3]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]^2-18*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]*s[3, 3]^2+54*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 2]^2*s[3, 3]+12*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]^3-12*s[1, 3]*s[2, 2]^4*s[3, 1]+24*s[1, 3]*s[2, 2]^3*s[3, 1]*s[3, 3]-60*s[1, 3]*s[2, 2]^2*s[2, 3]*s[3, 1]*s[3, 2]-6*s[1, 3]*s[2, 2]^2*s[3, 1]*s[3, 3]^2+6*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]-6*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]^3-36*s[1, 3]*s[2, 3]^2*s[3, 1]*s[3, 2]^2-6*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]^2-3*s[2, 2]^4*s[3, 3]^2+6*s[2, 2]^3*s[2, 3]*s[3, 2]*s[3, 3]+6*s[2, 2]^3*s[3, 3]^3-3*s[2, 2]^2*s[2, 3]^2*s[3, 2]^2-24*s[2, 2]^2*s[2, 3]*s[3, 2]*s[3, 3]^2-3*s[2, 2]^2*s[3, 3]^4+30*s[2, 2]*s[2, 3]^2*s[3, 2]^2*s[3, 3]+6*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]^3-12*s[2, 3]^3*s[3, 2]^3-3*s[2, 3]^2*s[3, 2]^2*s[3, 3]^2))^(1/3)+((1/3)*s[1, 1]*s[2, 2]+(1/3)*s[3, 3]*s[1, 1]-s[1, 2]*s[2, 1]-s[1, 3]*s[3, 1]+(1/3)*s[3, 3]*s[2, 2]-s[2, 3]*s[3, 2]-(1/3)*s[1, 1]^2-(1/3)*s[2, 2]^2-(1/3)*s[3, 3]^2)/(8*s[1, 1]^3-12*s[1, 1]^2*s[2, 2]-12*s[1, 1]^2*s[3, 3]+36*s[1, 1]*s[1, 2]*s[2, 1]+36*s[1, 1]*s[1, 3]*s[3, 1]-12*s[1, 1]*s[2, 2]^2+48*s[1, 1]*s[2, 2]*s[3, 3]-72*s[1, 1]*s[2, 3]*s[3, 2]-12*s[1, 1]*s[3, 3]^2+36*s[1, 2]*s[2, 1]*s[2, 2]-72*s[1, 2]*s[2, 1]*s[3, 3]+108*s[1, 2]*s[2, 3]*s[3, 1]+108*s[1, 3]*s[2, 1]*s[3, 2]-72*s[1, 3]*s[2, 2]*s[3, 1]+36*s[1, 3]*s[3, 1]*s[3, 3]+8*s[2, 2]^3-12*s[2, 2]^2*s[3, 3]+36*s[2, 2]*s[2, 3]*s[3, 2]-12*s[2, 2]*s[3, 3]^2+36*s[2, 3]*s[3, 2]*s[3, 3]+8*s[3, 3]^3+12*sqrt(-3*s[1, 1]^4*s[2, 2]^2+6*s[1, 1]^4*s[2, 2]*s[3, 3]-12*s[1, 1]^4*s[2, 3]*s[3, 2]-3*s[1, 1]^4*s[3, 3]^2+6*s[1, 1]^3*s[1, 2]*s[2, 1]*s[2, 2]-6*s[1, 1]^3*s[1, 2]*s[2, 1]*s[3, 3]+12*s[1, 1]^3*s[1, 2]*s[2, 3]*s[3, 1]+12*s[1, 1]^3*s[1, 3]*s[2, 1]*s[3, 2]-6*s[1, 1]^3*s[1, 3]*s[2, 2]*s[3, 1]+6*s[1, 1]^3*s[1, 3]*s[3, 1]*s[3, 3]+6*s[1, 1]^3*s[2, 2]^3-6*s[1, 1]^3*s[2, 2]^2*s[3, 3]+24*s[1, 1]^3*s[2, 2]*s[2, 3]*s[3, 2]-6*s[1, 1]^3*s[2, 2]*s[3, 3]^2+24*s[1, 1]^3*s[2, 3]*s[3, 2]*s[3, 3]+6*s[1, 1]^3*s[3, 3]^3-3*s[1, 1]^2*s[1, 2]^2*s[2, 1]^2-6*s[1, 1]^2*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]-24*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 2]^2+30*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]-60*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]-6*s[1, 1]^2*s[1, 2]*s[2, 1]*s[3, 3]^2-18*s[1, 1]^2*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]-18*s[1, 1]^2*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]-3*s[1, 1]^2*s[1, 3]^2*s[3, 1]^2-18*s[1, 1]^2*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]-18*s[1, 1]^2*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]-6*s[1, 1]^2*s[1, 3]*s[2, 2]^2*s[3, 1]+30*s[1, 1]^2*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]-60*s[1, 1]^2*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]-24*s[1, 1]^2*s[1, 3]*s[3, 1]*s[3, 3]^2-3*s[1, 1]^2*s[2, 2]^4-6*s[1, 1]^2*s[2, 2]^3*s[3, 3]-6*s[1, 1]^2*s[2, 2]^2*s[2, 3]*s[3, 2]+18*s[1, 1]^2*s[2, 2]^2*s[3, 3]^2-60*s[1, 1]^2*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]-6*s[1, 1]^2*s[2, 2]*s[3, 3]^3+24*s[1, 1]^2*s[2, 3]^2*s[3, 2]^2-6*s[1, 1]^2*s[2, 3]*s[3, 2]*s[3, 3]^2-3*s[1, 1]^2*s[3, 3]^4+30*s[1, 1]*s[1, 2]^2*s[2, 1]^2*s[2, 2]-24*s[1, 1]*s[1, 2]^2*s[2, 1]^2*s[3, 3]+54*s[1, 1]*s[1, 2]^2*s[2, 1]*s[2, 3]*s[3, 1]+54*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]^2*s[3, 2]+6*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 1]+6*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]*s[3, 3]+54*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 3]*s[3, 1]^2+6*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]^3+30*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]^2*s[3, 3]+6*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]-60*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]^2+114*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]*s[3, 3]+24*s[1, 1]*s[1, 2]*s[2, 1]*s[3, 3]^3-18*s[1, 1]*s[1, 2]*s[2, 2]^2*s[2, 3]*s[3, 1]+72*s[1, 1]*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 3]-108*s[1, 1]*s[1, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]-18*s[1, 1]*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]^2+54*s[1, 1]*s[1, 3]^2*s[2, 1]*s[3, 1]*s[3, 2]-24*s[1, 1]*s[1, 3]^2*s[2, 2]*s[3, 1]^2+30*s[1, 1]*s[1, 3]^2*s[3, 1]^2*s[3, 3]-18*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 2]+72*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]*s[3, 3]-108*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 2]^2-18*s[1, 1]*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]^2+24*s[1, 1]*s[1, 3]*s[2, 2]^3*s[3, 1]-60*s[1, 1]*s[1, 3]*s[2, 2]^2*s[3, 1]*s[3, 3]+114*s[1, 1]*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 2]+30*s[1, 1]*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]^2+6*s[1, 1]*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]+6*s[1, 1]*s[1, 3]*s[3, 1]*s[3, 3]^3+6*s[1, 1]*s[2, 2]^4*s[3, 3]-6*s[1, 1]*s[2, 2]^3*s[2, 3]*s[3, 2]-6*s[1, 1]*s[2, 2]^3*s[3, 3]^2+30*s[1, 1]*s[2, 2]^2*s[2, 3]*s[3, 2]*s[3, 3]-6*s[1, 1]*s[2, 2]^2*s[3, 3]^3-24*s[1, 1]*s[2, 2]*s[2, 3]^2*s[3, 2]^2+30*s[1, 1]*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]^2+6*s[1, 1]*s[2, 2]*s[3, 3]^4-24*s[1, 1]*s[2, 3]^2*s[3, 2]^2*s[3, 3]-6*s[1, 1]*s[2, 3]*s[3, 2]*s[3, 3]^3-12*s[1, 2]^3*s[2, 1]^3-36*s[1, 2]^2*s[1, 3]*s[2, 1]^2*s[3, 1]-3*s[1, 2]^2*s[2, 1]^2*s[2, 2]^2-24*s[1, 2]^2*s[2, 1]^2*s[2, 2]*s[3, 3]-36*s[1, 2]^2*s[2, 1]^2*s[2, 3]*s[3, 2]+24*s[1, 2]^2*s[2, 1]^2*s[3, 3]^2+54*s[1, 2]^2*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 1]-108*s[1, 2]^2*s[2, 1]*s[2, 3]*s[3, 1]*s[3, 3]+81*s[1, 2]^2*s[2, 3]^2*s[3, 1]^2-36*s[1, 2]*s[1, 3]^2*s[2, 1]*s[3, 1]^2+54*s[1, 2]*s[1, 3]*s[2, 1]^2*s[2, 2]*s[3, 2]-108*s[1, 2]*s[1, 3]*s[2, 1]^2*s[3, 2]*s[3, 3]-60*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 1]+114*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 1]*s[3, 3]+90*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 1]*s[3, 2]-60*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]*s[3, 3]^2-108*s[1, 2]*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]^2+54*s[1, 2]*s[1, 3]*s[2, 3]*s[3, 1]^2*s[3, 3]-6*s[1, 2]*s[2, 1]*s[2, 2]^3*s[3, 3]-6*s[1, 2]*s[2, 1]*s[2, 2]^2*s[2, 3]*s[3, 2]-6*s[1, 2]*s[2, 1]*s[2, 2]^2*s[3, 3]^2+6*s[1, 2]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]+24*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]^3-36*s[1, 2]*s[2, 1]*s[2, 3]^2*s[3, 2]^2-60*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]*s[3, 3]^2-12*s[1, 2]*s[2, 1]*s[3, 3]^4+12*s[1, 2]*s[2, 2]^3*s[2, 3]*s[3, 1]-18*s[1, 2]*s[2, 2]^2*s[2, 3]*s[3, 1]*s[3, 3]+54*s[1, 2]*s[2, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]-18*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 3]^2+54*s[1, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]*s[3, 3]+12*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]^3-12*s[1, 3]^3*s[3, 1]^3+81*s[1, 3]^2*s[2, 1]^2*s[3, 2]^2-108*s[1, 3]^2*s[2, 1]*s[2, 2]*s[3, 1]*s[3, 2]+54*s[1, 3]^2*s[2, 1]*s[3, 1]*s[3, 2]*s[3, 3]+24*s[1, 3]^2*s[2, 2]^2*s[3, 1]^2-24*s[1, 3]^2*s[2, 2]*s[3, 1]^2*s[3, 3]-36*s[1, 3]^2*s[2, 3]*s[3, 1]^2*s[3, 2]-3*s[1, 3]^2*s[3, 1]^2*s[3, 3]^2+12*s[1, 3]*s[2, 1]*s[2, 2]^3*s[3, 2]-18*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 2]*s[3, 3]+54*s[1, 3]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]^2-18*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]*s[3, 3]^2+54*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 2]^2*s[3, 3]+12*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]^3-12*s[1, 3]*s[2, 2]^4*s[3, 1]+24*s[1, 3]*s[2, 2]^3*s[3, 1]*s[3, 3]-60*s[1, 3]*s[2, 2]^2*s[2, 3]*s[3, 1]*s[3, 2]-6*s[1, 3]*s[2, 2]^2*s[3, 1]*s[3, 3]^2+6*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]-6*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]^3-36*s[1, 3]*s[2, 3]^2*s[3, 1]*s[3, 2]^2-6*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]^2-3*s[2, 2]^4*s[3, 3]^2+6*s[2, 2]^3*s[2, 3]*s[3, 2]*s[3, 3]+6*s[2, 2]^3*s[3, 3]^3-3*s[2, 2]^2*s[2, 3]^2*s[3, 2]^2-24*s[2, 2]^2*s[2, 3]*s[3, 2]*s[3, 3]^2-3*s[2, 2]^2*s[3, 3]^4+30*s[2, 2]*s[2, 3]^2*s[3, 2]^2*s[3, 3]+6*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]^3-12*s[2, 3]^3*s[3, 2]^3-3*s[2, 3]^2*s[3, 2]^2*s[3, 3]^2))^(1/3)+(1/3)*s[3, 3]+(1/3)*s[2, 2]+(1/3)*s[1, 1]-((1/2)*I)*sqrt(3)*((1/6)*(8*s[1, 1]^3-12*s[1, 1]^2*s[2, 2]-12*s[1, 1]^2*s[3, 3]+36*s[1, 1]*s[1, 2]*s[2, 1]+36*s[1, 1]*s[1, 3]*s[3, 1]-12*s[1, 1]*s[2, 2]^2+48*s[1, 1]*s[2, 2]*s[3, 3]-72*s[1, 1]*s[2, 3]*s[3, 2]-12*s[1, 1]*s[3, 3]^2+36*s[1, 2]*s[2, 1]*s[2, 2]-72*s[1, 2]*s[2, 1]*s[3, 3]+108*s[1, 2]*s[2, 3]*s[3, 1]+108*s[1, 3]*s[2, 1]*s[3, 2]-72*s[1, 3]*s[2, 2]*s[3, 1]+36*s[1, 3]*s[3, 1]*s[3, 3]+8*s[2, 2]^3-12*s[2, 2]^2*s[3, 3]+36*s[2, 2]*s[2, 3]*s[3, 2]-12*s[2, 2]*s[3, 3]^2+36*s[2, 3]*s[3, 2]*s[3, 3]+8*s[3, 3]^3+12*sqrt(-3*s[1, 1]^4*s[2, 2]^2+6*s[1, 1]^4*s[2, 2]*s[3, 3]-12*s[1, 1]^4*s[2, 3]*s[3, 2]-3*s[1, 1]^4*s[3, 3]^2+6*s[1, 1]^3*s[1, 2]*s[2, 1]*s[2, 2]-6*s[1, 1]^3*s[1, 2]*s[2, 1]*s[3, 3]+12*s[1, 1]^3*s[1, 2]*s[2, 3]*s[3, 1]+12*s[1, 1]^3*s[1, 3]*s[2, 1]*s[3, 2]-6*s[1, 1]^3*s[1, 3]*s[2, 2]*s[3, 1]+6*s[1, 1]^3*s[1, 3]*s[3, 1]*s[3, 3]+6*s[1, 1]^3*s[2, 2]^3-6*s[1, 1]^3*s[2, 2]^2*s[3, 3]+24*s[1, 1]^3*s[2, 2]*s[2, 3]*s[3, 2]-6*s[1, 1]^3*s[2, 2]*s[3, 3]^2+24*s[1, 1]^3*s[2, 3]*s[3, 2]*s[3, 3]+6*s[1, 1]^3*s[3, 3]^3-3*s[1, 1]^2*s[1, 2]^2*s[2, 1]^2-6*s[1, 1]^2*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]-24*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 2]^2+30*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]-60*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]-6*s[1, 1]^2*s[1, 2]*s[2, 1]*s[3, 3]^2-18*s[1, 1]^2*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]-18*s[1, 1]^2*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]-3*s[1, 1]^2*s[1, 3]^2*s[3, 1]^2-18*s[1, 1]^2*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]-18*s[1, 1]^2*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]-6*s[1, 1]^2*s[1, 3]*s[2, 2]^2*s[3, 1]+30*s[1, 1]^2*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]-60*s[1, 1]^2*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]-24*s[1, 1]^2*s[1, 3]*s[3, 1]*s[3, 3]^2-3*s[1, 1]^2*s[2, 2]^4-6*s[1, 1]^2*s[2, 2]^3*s[3, 3]-6*s[1, 1]^2*s[2, 2]^2*s[2, 3]*s[3, 2]+18*s[1, 1]^2*s[2, 2]^2*s[3, 3]^2-60*s[1, 1]^2*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]-6*s[1, 1]^2*s[2, 2]*s[3, 3]^3+24*s[1, 1]^2*s[2, 3]^2*s[3, 2]^2-6*s[1, 1]^2*s[2, 3]*s[3, 2]*s[3, 3]^2-3*s[1, 1]^2*s[3, 3]^4+30*s[1, 1]*s[1, 2]^2*s[2, 1]^2*s[2, 2]-24*s[1, 1]*s[1, 2]^2*s[2, 1]^2*s[3, 3]+54*s[1, 1]*s[1, 2]^2*s[2, 1]*s[2, 3]*s[3, 1]+54*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]^2*s[3, 2]+6*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 1]+6*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]*s[3, 3]+54*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 3]*s[3, 1]^2+6*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]^3+30*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]^2*s[3, 3]+6*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]-60*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]^2+114*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]*s[3, 3]+24*s[1, 1]*s[1, 2]*s[2, 1]*s[3, 3]^3-18*s[1, 1]*s[1, 2]*s[2, 2]^2*s[2, 3]*s[3, 1]+72*s[1, 1]*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 3]-108*s[1, 1]*s[1, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]-18*s[1, 1]*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]^2+54*s[1, 1]*s[1, 3]^2*s[2, 1]*s[3, 1]*s[3, 2]-24*s[1, 1]*s[1, 3]^2*s[2, 2]*s[3, 1]^2+30*s[1, 1]*s[1, 3]^2*s[3, 1]^2*s[3, 3]-18*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 2]+72*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]*s[3, 3]-108*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 2]^2-18*s[1, 1]*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]^2+24*s[1, 1]*s[1, 3]*s[2, 2]^3*s[3, 1]-60*s[1, 1]*s[1, 3]*s[2, 2]^2*s[3, 1]*s[3, 3]+114*s[1, 1]*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 2]+30*s[1, 1]*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]^2+6*s[1, 1]*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]+6*s[1, 1]*s[1, 3]*s[3, 1]*s[3, 3]^3+6*s[1, 1]*s[2, 2]^4*s[3, 3]-6*s[1, 1]*s[2, 2]^3*s[2, 3]*s[3, 2]-6*s[1, 1]*s[2, 2]^3*s[3, 3]^2+30*s[1, 1]*s[2, 2]^2*s[2, 3]*s[3, 2]*s[3, 3]-6*s[1, 1]*s[2, 2]^2*s[3, 3]^3-24*s[1, 1]*s[2, 2]*s[2, 3]^2*s[3, 2]^2+30*s[1, 1]*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]^2+6*s[1, 1]*s[2, 2]*s[3, 3]^4-24*s[1, 1]*s[2, 3]^2*s[3, 2]^2*s[3, 3]-6*s[1, 1]*s[2, 3]*s[3, 2]*s[3, 3]^3-12*s[1, 2]^3*s[2, 1]^3-36*s[1, 2]^2*s[1, 3]*s[2, 1]^2*s[3, 1]-3*s[1, 2]^2*s[2, 1]^2*s[2, 2]^2-24*s[1, 2]^2*s[2, 1]^2*s[2, 2]*s[3, 3]-36*s[1, 2]^2*s[2, 1]^2*s[2, 3]*s[3, 2]+24*s[1, 2]^2*s[2, 1]^2*s[3, 3]^2+54*s[1, 2]^2*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 1]-108*s[1, 2]^2*s[2, 1]*s[2, 3]*s[3, 1]*s[3, 3]+81*s[1, 2]^2*s[2, 3]^2*s[3, 1]^2-36*s[1, 2]*s[1, 3]^2*s[2, 1]*s[3, 1]^2+54*s[1, 2]*s[1, 3]*s[2, 1]^2*s[2, 2]*s[3, 2]-108*s[1, 2]*s[1, 3]*s[2, 1]^2*s[3, 2]*s[3, 3]-60*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 1]+114*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 1]*s[3, 3]+90*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 1]*s[3, 2]-60*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]*s[3, 3]^2-108*s[1, 2]*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]^2+54*s[1, 2]*s[1, 3]*s[2, 3]*s[3, 1]^2*s[3, 3]-6*s[1, 2]*s[2, 1]*s[2, 2]^3*s[3, 3]-6*s[1, 2]*s[2, 1]*s[2, 2]^2*s[2, 3]*s[3, 2]-6*s[1, 2]*s[2, 1]*s[2, 2]^2*s[3, 3]^2+6*s[1, 2]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]+24*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]^3-36*s[1, 2]*s[2, 1]*s[2, 3]^2*s[3, 2]^2-60*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]*s[3, 3]^2-12*s[1, 2]*s[2, 1]*s[3, 3]^4+12*s[1, 2]*s[2, 2]^3*s[2, 3]*s[3, 1]-18*s[1, 2]*s[2, 2]^2*s[2, 3]*s[3, 1]*s[3, 3]+54*s[1, 2]*s[2, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]-18*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 3]^2+54*s[1, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]*s[3, 3]+12*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]^3-12*s[1, 3]^3*s[3, 1]^3+81*s[1, 3]^2*s[2, 1]^2*s[3, 2]^2-108*s[1, 3]^2*s[2, 1]*s[2, 2]*s[3, 1]*s[3, 2]+54*s[1, 3]^2*s[2, 1]*s[3, 1]*s[3, 2]*s[3, 3]+24*s[1, 3]^2*s[2, 2]^2*s[3, 1]^2-24*s[1, 3]^2*s[2, 2]*s[3, 1]^2*s[3, 3]-36*s[1, 3]^2*s[2, 3]*s[3, 1]^2*s[3, 2]-3*s[1, 3]^2*s[3, 1]^2*s[3, 3]^2+12*s[1, 3]*s[2, 1]*s[2, 2]^3*s[3, 2]-18*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 2]*s[3, 3]+54*s[1, 3]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]^2-18*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]*s[3, 3]^2+54*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 2]^2*s[3, 3]+12*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]^3-12*s[1, 3]*s[2, 2]^4*s[3, 1]+24*s[1, 3]*s[2, 2]^3*s[3, 1]*s[3, 3]-60*s[1, 3]*s[2, 2]^2*s[2, 3]*s[3, 1]*s[3, 2]-6*s[1, 3]*s[2, 2]^2*s[3, 1]*s[3, 3]^2+6*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]-6*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]^3-36*s[1, 3]*s[2, 3]^2*s[3, 1]*s[3, 2]^2-6*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]^2-3*s[2, 2]^4*s[3, 3]^2+6*s[2, 2]^3*s[2, 3]*s[3, 2]*s[3, 3]+6*s[2, 2]^3*s[3, 3]^3-3*s[2, 2]^2*s[2, 3]^2*s[3, 2]^2-24*s[2, 2]^2*s[2, 3]*s[3, 2]*s[3, 3]^2-3*s[2, 2]^2*s[3, 3]^4+30*s[2, 2]*s[2, 3]^2*s[3, 2]^2*s[3, 3]+6*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]^3-12*s[2, 3]^3*s[3, 2]^3-3*s[2, 3]^2*s[3, 2]^2*s[3, 3]^2))^(1/3)+((2/3)*s[1, 1]*s[2, 2]+(2/3)*s[3, 3]*s[1, 1]-2*s[1, 2]*s[2, 1]-2*s[1, 3]*s[3, 1]+(2/3)*s[3, 3]*s[2, 2]-2*s[2, 3]*s[3, 2]-(2/3)*s[1, 1]^2-(2/3)*s[2, 2]^2-(2/3)*s[3, 3]^2)/(8*s[1, 1]^3-12*s[1, 1]^2*s[2, 2]-12*s[1, 1]^2*s[3, 3]+36*s[1, 1]*s[1, 2]*s[2, 1]+36*s[1, 1]*s[1, 3]*s[3, 1]-12*s[1, 1]*s[2, 2]^2+48*s[1, 1]*s[2, 2]*s[3, 3]-72*s[1, 1]*s[2, 3]*s[3, 2]-12*s[1, 1]*s[3, 3]^2+36*s[1, 2]*s[2, 1]*s[2, 2]-72*s[1, 2]*s[2, 1]*s[3, 3]+108*s[1, 2]*s[2, 3]*s[3, 1]+108*s[1, 3]*s[2, 1]*s[3, 2]-72*s[1, 3]*s[2, 2]*s[3, 1]+36*s[1, 3]*s[3, 1]*s[3, 3]+8*s[2, 2]^3-12*s[2, 2]^2*s[3, 3]+36*s[2, 2]*s[2, 3]*s[3, 2]-12*s[2, 2]*s[3, 3]^2+36*s[2, 3]*s[3, 2]*s[3, 3]+8*s[3, 3]^3+12*sqrt(-3*s[1, 1]^4*s[2, 2]^2+6*s[1, 1]^4*s[2, 2]*s[3, 3]-12*s[1, 1]^4*s[2, 3]*s[3, 2]-3*s[1, 1]^4*s[3, 3]^2+6*s[1, 1]^3*s[1, 2]*s[2, 1]*s[2, 2]-6*s[1, 1]^3*s[1, 2]*s[2, 1]*s[3, 3]+12*s[1, 1]^3*s[1, 2]*s[2, 3]*s[3, 1]+12*s[1, 1]^3*s[1, 3]*s[2, 1]*s[3, 2]-6*s[1, 1]^3*s[1, 3]*s[2, 2]*s[3, 1]+6*s[1, 1]^3*s[1, 3]*s[3, 1]*s[3, 3]+6*s[1, 1]^3*s[2, 2]^3-6*s[1, 1]^3*s[2, 2]^2*s[3, 3]+24*s[1, 1]^3*s[2, 2]*s[2, 3]*s[3, 2]-6*s[1, 1]^3*s[2, 2]*s[3, 3]^2+24*s[1, 1]^3*s[2, 3]*s[3, 2]*s[3, 3]+6*s[1, 1]^3*s[3, 3]^3-3*s[1, 1]^2*s[1, 2]^2*s[2, 1]^2-6*s[1, 1]^2*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]-24*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 2]^2+30*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]-60*s[1, 1]^2*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]-6*s[1, 1]^2*s[1, 2]*s[2, 1]*s[3, 3]^2-18*s[1, 1]^2*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]-18*s[1, 1]^2*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]-3*s[1, 1]^2*s[1, 3]^2*s[3, 1]^2-18*s[1, 1]^2*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]-18*s[1, 1]^2*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]-6*s[1, 1]^2*s[1, 3]*s[2, 2]^2*s[3, 1]+30*s[1, 1]^2*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]-60*s[1, 1]^2*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]-24*s[1, 1]^2*s[1, 3]*s[3, 1]*s[3, 3]^2-3*s[1, 1]^2*s[2, 2]^4-6*s[1, 1]^2*s[2, 2]^3*s[3, 3]-6*s[1, 1]^2*s[2, 2]^2*s[2, 3]*s[3, 2]+18*s[1, 1]^2*s[2, 2]^2*s[3, 3]^2-60*s[1, 1]^2*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]-6*s[1, 1]^2*s[2, 2]*s[3, 3]^3+24*s[1, 1]^2*s[2, 3]^2*s[3, 2]^2-6*s[1, 1]^2*s[2, 3]*s[3, 2]*s[3, 3]^2-3*s[1, 1]^2*s[3, 3]^4+30*s[1, 1]*s[1, 2]^2*s[2, 1]^2*s[2, 2]-24*s[1, 1]*s[1, 2]^2*s[2, 1]^2*s[3, 3]+54*s[1, 1]*s[1, 2]^2*s[2, 1]*s[2, 3]*s[3, 1]+54*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]^2*s[3, 2]+6*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 1]+6*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]*s[3, 3]+54*s[1, 1]*s[1, 2]*s[1, 3]*s[2, 3]*s[3, 1]^2+6*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]^3+30*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]^2*s[3, 3]+6*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]-60*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]^2+114*s[1, 1]*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]*s[3, 3]+24*s[1, 1]*s[1, 2]*s[2, 1]*s[3, 3]^3-18*s[1, 1]*s[1, 2]*s[2, 2]^2*s[2, 3]*s[3, 1]+72*s[1, 1]*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 3]-108*s[1, 1]*s[1, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]-18*s[1, 1]*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]^2+54*s[1, 1]*s[1, 3]^2*s[2, 1]*s[3, 1]*s[3, 2]-24*s[1, 1]*s[1, 3]^2*s[2, 2]*s[3, 1]^2+30*s[1, 1]*s[1, 3]^2*s[3, 1]^2*s[3, 3]-18*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 2]+72*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]*s[3, 3]-108*s[1, 1]*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 2]^2-18*s[1, 1]*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]^2+24*s[1, 1]*s[1, 3]*s[2, 2]^3*s[3, 1]-60*s[1, 1]*s[1, 3]*s[2, 2]^2*s[3, 1]*s[3, 3]+114*s[1, 1]*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 2]+30*s[1, 1]*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]^2+6*s[1, 1]*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]+6*s[1, 1]*s[1, 3]*s[3, 1]*s[3, 3]^3+6*s[1, 1]*s[2, 2]^4*s[3, 3]-6*s[1, 1]*s[2, 2]^3*s[2, 3]*s[3, 2]-6*s[1, 1]*s[2, 2]^3*s[3, 3]^2+30*s[1, 1]*s[2, 2]^2*s[2, 3]*s[3, 2]*s[3, 3]-6*s[1, 1]*s[2, 2]^2*s[3, 3]^3-24*s[1, 1]*s[2, 2]*s[2, 3]^2*s[3, 2]^2+30*s[1, 1]*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]^2+6*s[1, 1]*s[2, 2]*s[3, 3]^4-24*s[1, 1]*s[2, 3]^2*s[3, 2]^2*s[3, 3]-6*s[1, 1]*s[2, 3]*s[3, 2]*s[3, 3]^3-12*s[1, 2]^3*s[2, 1]^3-36*s[1, 2]^2*s[1, 3]*s[2, 1]^2*s[3, 1]-3*s[1, 2]^2*s[2, 1]^2*s[2, 2]^2-24*s[1, 2]^2*s[2, 1]^2*s[2, 2]*s[3, 3]-36*s[1, 2]^2*s[2, 1]^2*s[2, 3]*s[3, 2]+24*s[1, 2]^2*s[2, 1]^2*s[3, 3]^2+54*s[1, 2]^2*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 1]-108*s[1, 2]^2*s[2, 1]*s[2, 3]*s[3, 1]*s[3, 3]+81*s[1, 2]^2*s[2, 3]^2*s[3, 1]^2-36*s[1, 2]*s[1, 3]^2*s[2, 1]*s[3, 1]^2+54*s[1, 2]*s[1, 3]*s[2, 1]^2*s[2, 2]*s[3, 2]-108*s[1, 2]*s[1, 3]*s[2, 1]^2*s[3, 2]*s[3, 3]-60*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 1]+114*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 1]*s[3, 3]+90*s[1, 2]*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 1]*s[3, 2]-60*s[1, 2]*s[1, 3]*s[2, 1]*s[3, 1]*s[3, 3]^2-108*s[1, 2]*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]^2+54*s[1, 2]*s[1, 3]*s[2, 3]*s[3, 1]^2*s[3, 3]-6*s[1, 2]*s[2, 1]*s[2, 2]^3*s[3, 3]-6*s[1, 2]*s[2, 1]*s[2, 2]^2*s[2, 3]*s[3, 2]-6*s[1, 2]*s[2, 1]*s[2, 2]^2*s[3, 3]^2+6*s[1, 2]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]+24*s[1, 2]*s[2, 1]*s[2, 2]*s[3, 3]^3-36*s[1, 2]*s[2, 1]*s[2, 3]^2*s[3, 2]^2-60*s[1, 2]*s[2, 1]*s[2, 3]*s[3, 2]*s[3, 3]^2-12*s[1, 2]*s[2, 1]*s[3, 3]^4+12*s[1, 2]*s[2, 2]^3*s[2, 3]*s[3, 1]-18*s[1, 2]*s[2, 2]^2*s[2, 3]*s[3, 1]*s[3, 3]+54*s[1, 2]*s[2, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]-18*s[1, 2]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 3]^2+54*s[1, 2]*s[2, 3]^2*s[3, 1]*s[3, 2]*s[3, 3]+12*s[1, 2]*s[2, 3]*s[3, 1]*s[3, 3]^3-12*s[1, 3]^3*s[3, 1]^3+81*s[1, 3]^2*s[2, 1]^2*s[3, 2]^2-108*s[1, 3]^2*s[2, 1]*s[2, 2]*s[3, 1]*s[3, 2]+54*s[1, 3]^2*s[2, 1]*s[3, 1]*s[3, 2]*s[3, 3]+24*s[1, 3]^2*s[2, 2]^2*s[3, 1]^2-24*s[1, 3]^2*s[2, 2]*s[3, 1]^2*s[3, 3]-36*s[1, 3]^2*s[2, 3]*s[3, 1]^2*s[3, 2]-3*s[1, 3]^2*s[3, 1]^2*s[3, 3]^2+12*s[1, 3]*s[2, 1]*s[2, 2]^3*s[3, 2]-18*s[1, 3]*s[2, 1]*s[2, 2]^2*s[3, 2]*s[3, 3]+54*s[1, 3]*s[2, 1]*s[2, 2]*s[2, 3]*s[3, 2]^2-18*s[1, 3]*s[2, 1]*s[2, 2]*s[3, 2]*s[3, 3]^2+54*s[1, 3]*s[2, 1]*s[2, 3]*s[3, 2]^2*s[3, 3]+12*s[1, 3]*s[2, 1]*s[3, 2]*s[3, 3]^3-12*s[1, 3]*s[2, 2]^4*s[3, 1]+24*s[1, 3]*s[2, 2]^3*s[3, 1]*s[3, 3]-60*s[1, 3]*s[2, 2]^2*s[2, 3]*s[3, 1]*s[3, 2]-6*s[1, 3]*s[2, 2]^2*s[3, 1]*s[3, 3]^2+6*s[1, 3]*s[2, 2]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]-6*s[1, 3]*s[2, 2]*s[3, 1]*s[3, 3]^3-36*s[1, 3]*s[2, 3]^2*s[3, 1]*s[3, 2]^2-6*s[1, 3]*s[2, 3]*s[3, 1]*s[3, 2]*s[3, 3]^2-3*s[2, 2]^4*s[3, 3]^2+6*s[2, 2]^3*s[2, 3]*s[3, 2]*s[3, 3]+6*s[2, 2]^3*s[3, 3]^3-3*s[2, 2]^2*s[2, 3]^2*s[3, 2]^2-24*s[2, 2]^2*s[2, 3]*s[3, 2]*s[3, 3]^2-3*s[2, 2]^2*s[3, 3]^4+30*s[2, 2]*s[2, 3]^2*s[3, 2]^2*s[3, 3]+6*s[2, 2]*s[2, 3]*s[3, 2]*s[3, 3]^3-12*s[2, 3]^3*s[3, 2]^3-3*s[2, 3]^2*s[3, 2]^2*s[3, 3]^2))^(1/3))})

(2)

restart

with(LinearAlgebra):

for N from 2 to 5 do
  M       := RandomMatrix(N, generator=-2^31..2^31);
  eig_||N := CodeTools:-Usage( Eigenvalues(M) ):
  print(length(eig_||N)):
end do:

memory used=2.99MiB, alloc change=32.00MiB, cpu time=77.00ms, real time=520.00ms, gc time=8.46ms

 

126

 

memory used=2.84MiB, alloc change=0 bytes, cpu time=84.00ms, real time=2.71s, gc time=0ns

 

1345

 

memory used=2.88MiB, alloc change=0 bytes, cpu time=44.00ms, real time=440.00ms, gc time=0ns

 

17144

 

memory used=2.42MiB, alloc change=0 bytes, cpu time=27.00ms, real time=103.00ms, gc time=0ns

 

1046

(3)

# uncomment to understand why the size of eig_4 is much larger than the size of eig_5
eig_4:
eig_5:

restart

with(LinearAlgebra):

for N from 2 to 5 do
  M       := RandomMatrix(N, generator=-2.0^31..2.0^31);
  eig_||N := CodeTools:-Usage( Eigenvalues(M) ):
  print(length(eig_||N)):
end do:

memory used=1.84MiB, alloc change=0 bytes, cpu time=47.00ms, real time=1.25s, gc time=0ns

 

30

 

memory used=74.70KiB, alloc change=0 bytes, cpu time=1000.00us, real time=48.00ms, gc time=0ns

 

32

 

memory used=74.98KiB, alloc change=0 bytes, cpu time=1000.00us, real time=0ns, gc time=0ns

 

34

 

memory used=75.34KiB, alloc change=0 bytes, cpu time=1000.00us, real time=0ns, gc time=0ns

 

36

(4)

 


 

Download Eigenvalues.mw


Eigenvalues.mw

@hajnayeb 

Sorry for the late,

The last parameter in procedure KG (1 presently) corresponds to the standard deviation of the gaussian process (your white noise if the third parameter is set to a small value).
 

@vv 
You're right I was over optimistic thinking  that could exist only one solution.
 

UNDERSTOOD

 

The problem comes from the "leading" term X(t)*diff(X(t), t$2).
Maple isolates the differential termes of higher order and transforms the ode into 
diff(X(t), t$2) =( diff(X(t),t)/(1+diff(X(t),t)^2) + F) / X(t) ... wich, given ths ics,  equals (1/2-1/2)/0 = "0/0" 
Not a sinularity but an undefined form: maybe I would have waste less time with a more explicity error message?

Starting from 0 with X(0)="a small value" fixes the problem.

Now another issue: how can I found a numerical solution closer to the exact one on the range 0..T for T larger than 1 (the true solution converges asymptotically to 0 as T -> infinity)?
 


 

restart

interface(version)

`Standard Worksheet Interface, Maple 2015.2, Mac OS X, December 21 2015 Build ID 1097895`

(1)

with(plots):

# Source term

F := t*(-600*t/(100*t^2+1)^2+80000*t^3/(100*t^2+1)^3)/(100*t^2+1)-(1/(100*t^2+1)-200*t^2/(100*t^2+1)^2)/(1+(1/(100*t^2+1)-200*t^2/(100*t^2+1)^2)^2);

# plot(F, t=0..0.5);

t*(-600*t/(100*t^2+1)^2+80000*t^3/(100*t^2+1)^3)/(100*t^2+1)-(1/(100*t^2+1)-200*t^2/(100*t^2+1)^2)/(1+(1/(100*t^2+1)-200*t^2/(100*t^2+1)^2)^2)

(2)

# Ode

ode := X(t)*diff(X(t), t$2)-diff(X(t),t)/(1+diff(X(t),t)^2) - 'F';

X(t)*(diff(diff(X(t), t), t))-(diff(X(t), t))/(1+(diff(X(t), t))^2)-F

(3)

# Initial conditions


eps := 1e-10:
ics := X(0) = eps, D(X)(0) = 1

X(0) = 0.1e-9, (D(X))(0) = 1

(4)

# The solution must be this one

U := t -> t/((t*10)^2+1)

proc (t) options operator, arrow; t/(100*t^2+1) end proc

(5)

# Check ode and ics

eval(ode, X(t)=U(t));
U(0);
D(U)(0);

0

 

0

 

1

(6)

# Plots

meths  := [rkf45, dverk78, rosenbrock, lsode]:
colors := table([rkf45=red, dverk78=gold, rosenbrock=green, lsode=cyan]):

for meth in meths do
  sol_||meth := dsolve({ode, ics}, numeric, method=meth):
end do:

display(
  plot(U(t), t=0..1, color=blue, legend=exact),
  seq( odeplot(sol_||meth, [t, X(t)], t=0..1, color=red, linestyle=3, color=colors[meth], legend=meth), meth in meths )
);

 

# Starting from t=0.4 doesn't help to obtain good numerical solutions

ics_2 := X(0.4) = U(0.4), D(X)(0.4) = eval(diff(U(t), t), t=0.4);

for meth in meths do
  sol_||meth := dsolve({ode, ics_2}, numeric, method=meth):
end do:

display(
  plot(U(t), t=0.4..1, color=blue, legend=exact),
  seq( odeplot(sol_||meth, [t, X(t)], t=0.4..1, color=red, linestyle=3, color=colors[meth], legend=meth), meth in meths )
);

X(.4) = 0.2352941176e-1, (D(X))(.4) = -0.5190311419e-1

 

Warning, could not obtain numerical solution at all points, plot may be incomplete

 

Warning, cannot evaluate the solution further right of .72054998, probably a singularity

 

Warning, could not obtain numerical solution at all points, plot may be incomplete

 

 

 


 

Download Unsuccessful_dsolve_2.mw

I aggree with what said before.

Here are just a few "statistics" about the 15 by 15 polynomial system you want to find a Grobner basis of.

Polynoms 14 and 15 have 14080 terms and require each 704241 words to be represented.
Their total degrees are both 18 and the most complex monomial they contain is the product of 11 indeterminates.

So it doesn't seem strange to me that Maple might face enormous difficulties to compute a Grobner basis and that it ends up ends by  some crash.
I even doubt that CAS specialized in GB computations could handle this?
 

restart;

with(LinearAlgebra):

F0:=(w*f00+v*f01)/(v+w):
F1:=(u*f10+w*f11)/(w+u):
F2:=(v*f20+u*f21)/(u+v):
T:=(u)^(3)*p0+(v)^(3)*p1+(w)^(3)*p2 + 3*u*v*(u+v)*(u*e01+v*e10) + 3*v*w*(v+w)*(v*e11+w*e20) + 3*w*u*(w+u)*(w*e21+u*e00) + 12*u*v*w*(u*F0+v*F1+w*F2):
coefList:=[p0,p1,p2,e00,e01,e10,e11,e20,e21,f00,f01,f10,f11,f20,f21]:
nops(coefList):

for i from 1 to nops(coefList) do
 ind:=coefList[i];
  BF||ind:=subs(w=1-u-v, factor(coeff(T,coefList[i],1)));
end do:

for i from 1 to nops(coefList) do
 ind:=coefList[i];
 DDBF||ind:=factor(diff(BF||ind,u,v));
end do:

QR:=x-> t1*subs(u=u1,v=v1,x) + t2*subs(u=u2,v=v2,x) + t3*subs(u=u3,v=v3,x) + (t4)*subs(u=u4,v=v4,x)+t5*subs(u=u5,v=v5,x):

for i from 1 to nops(coefList) do
 ind:=coefList[i];
 eq[i]:=numer(simplify(int(DDBF||ind, u=0..1-v, v=0..1) - QR(DDBF||ind)));
end do:

sys := [seq(eq[i],i=1..nops(coefList))]:
nops(sys);
nops(coefList);

15

 

15

(1)

# number of terms in each eq[i]

seq(nops(eq[i]),i=1..nops(coefList));

# number of words used to represent each eq[i]
seq(length(eq[i]),i=1..nops(coefList));

# total degree of each eq[i]

seq(degree(eq[i]),i=1..nops(coefList));

# total degree of each eq[i]

seq(degree(eq[i]),i=1..nops(coefList));

# maximum number of indeterminates in the monomials of each eq[i]

ni := NULL:
for i from 1 to nops(coefList) do
  nj := 0:
  for j from 1 to nops(eq[i]) do
    nj := max(nj, numelems(indets(op(j, eq[i]), name)))
  end do;
  ni := ni, nj
end do:
ni;

1, 1, 16, 16, 11, 11, 16, 30, 30, 3645, 2268, 2268, 3645, 14080, 14080

 

0, 0, 170, 255, 180, 180, 255, 416, 416, 115876, 73669, 73669, 115876, 704241, 704241

 

-infinity, -infinity, 2, 3, 3, 3, 3, 3, 3, 13, 13, 13, 13, 18, 18

 

-infinity, -infinity, 2, 3, 3, 3, 3, 3, 3, 13, 13, 13, 13, 18, 18

 

0, 0, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 11, 11

(2)

 


 

Download GB.mw

@Adam Ledger 

Watchout, the output (5) is not the one of CF_LS  but print's.
I have removed the print instruction, replaced the colon at the end of the line CF_LS :=... by a semicolon, and right clicked on the output.
Here is the result.


PS: I'm not familiar with the 2D input mode and I never use it. 

restart:

with(numtheory):

S[0] := proc (N, K) options operator, arrow; map(simplify, {seq(seq(seq(piecewise((a^varphi(b))^(1/(c+1))-floor((a^varphi(b))^(1/(c+1))) = 0, [a, b, c], NULL), a = 1 .. N), b = 1 .. N), c = 1 .. K)}, 'radical') end proc

proc (N, K) options operator, arrow; map(simplify, {seq(seq(seq(piecewise((a^numtheory:-varphi(b))^(1/(c+1))-floor((a^numtheory:-varphi(b))^(1/(c+1))) = 0, [a, b, c], NULL), a = 1 .. N), b = 1 .. N), c = 1 .. K)}, 'radical') end proc

(1)

T := proc (N, K) options operator, arrow; {seq(seq(seq([a, b, c], a = 1 .. N), b = 1 .. N), c = 1 .. K)} end proc

proc (N, K) options operator, arrow; {seq(seq(seq([a, b, c], a = 1 .. N), b = 1 .. N), c = 1 .. K)} end proc

(2)

S[1] := proc (N, K) options operator, arrow; `minus`(T(N, K), S[0](N, K)) end proc

proc (N, K) options operator, arrow; `minus`(T(N, K), S[0](N, K)) end proc

(3)

CardRatio := proc (N, K) options operator, arrow; nops(S[0](N, K))/nops(S[1](N, K)) end proc

proc (N, K) options operator, arrow; nops(S[0](N, K))/nops(S[1](N, K)) end proc

(4)

CF_LS := [
           CurveFitting[LeastSquares]([seq([k, CardRatio(2, k)], k = 1 .. 10)], K),
           CurveFitting[LeastSquares]([seq([k, CardRatio(3, k)], k = 1 .. 10)], K),
           CurveFitting[LeastSquares]([seq([k, CardRatio(4, k)], k = 1 .. 10)], K)
         ];

[1, 44268857/45401356-(532409481/9988298320)*K, 24308311919/13309971675-(135902619982/773879781675)*K]

(5)

smartplot( (5) );

 

# Maybe it would be better to do somethink like this?

colors := [red, green, blue]:

plots:-display(
  seq( plot(CF_LS[k], color=colors[k], legend=cat("Cardio(", k+1, ")")), k=1..3)
)

 

 


 

Download numtheory.mw

@Preben Alsholm 

No code missing, phi is the totient function, @Adam Ledger has just omited to say that.

So Adam's code run correctly after loading the numtheory package but I don't understand what Adam  wants?
 

restart:

with(numtheory):

S[0] := proc (N, K) options operator, arrow; map(simplify, {seq(seq(seq(piecewise((a^varphi(b))^(1/(c+1))-floor((a^varphi(b))^(1/(c+1))) = 0, [a, b, c], NULL), a = 1 .. N), b = 1 .. N), c = 1 .. K)}, 'radical') end proc

proc (N, K) options operator, arrow; map(simplify, {seq(seq(seq(piecewise((a^numtheory:-varphi(b))^(1/(c+1))-floor((a^numtheory:-varphi(b))^(1/(c+1))) = 0, [a, b, c], NULL), a = 1 .. N), b = 1 .. N), c = 1 .. K)}, 'radical') end proc

(1)

T := proc (N, K) options operator, arrow; {seq(seq(seq([a, b, c], a = 1 .. N), b = 1 .. N), c = 1 .. K)} end proc

proc (N, K) options operator, arrow; {seq(seq(seq([a, b, c], a = 1 .. N), b = 1 .. N), c = 1 .. K)} end proc

(2)

S[1] := proc (N, K) options operator, arrow; `minus`(T(N, K), S[0](N, K)) end proc

proc (N, K) options operator, arrow; `minus`(T(N, K), S[0](N, K)) end proc

(3)

CardRatio := proc (N, K) options operator, arrow; nops(S[0](N, K))/nops(S[1](N, K)) end proc

proc (N, K) options operator, arrow; nops(S[0](N, K))/nops(S[1](N, K)) end proc

(4)

CF_LS := {
           CurveFitting[LeastSquares]([seq([k, CardRatio(2, k)], k = 1 .. 10)], K),
           CurveFitting[LeastSquares]([seq([k, CardRatio(3, k)], k = 1 .. 10)], K),
           CurveFitting[LeastSquares]([seq([k, CardRatio(4, k)], k = 1 .. 10)], K)
         }:
print~(CF_LS):

1

 

44268857/45401356-(532409481/9988298320)*K

 

24308311919/13309971675-(135902619982/773879781675)*K

(5)

 

 

Download numtheory.mw

That's impossible : -2/(15*h) -1/(6*h) + 3/(10*h) = 0, thus the result you should want is 0, not 4*epsilon/(15*h)


 

restart

expr := -2*f(x-2*h)/15/h-f(x)/6/h+3*f(x+3*h)/10/h+2*ff(x-2*h)/15/h+ff(x)/6/h-3*ff(x+3*h)/10/h

-(2/15)*f(x-2*h)/h-(1/6)*f(x)/h+(3/10)*f(x+3*h)/h+(2/15)*ff(x-2*h)/h+(1/6)*ff(x)/h-(3/10)*ff(x+3*h)/h

(1)

MyRules := { seq(f(x+i*h)=ff(x+i*h)+epsilon, i=-2..3) };

{f(x) = ff(x)+epsilon, f(-h+x) = ff(-h+x)+epsilon, f(h+x) = ff(h+x)+epsilon, f(2*h+x) = ff(2*h+x)+epsilon, f(x-2*h) = ff(x-2*h)+epsilon, f(x+3*h) = ff(x+3*h)+epsilon}

(2)

subs(MyRules, expr);

-(2/15)*(ff(x-2*h)+epsilon)/h-(1/6)*(ff(x)+epsilon)/h+(3/10)*(ff(x+3*h)+epsilon)/h+(2/15)*ff(x-2*h)/h+(1/6)*ff(x)/h-(3/10)*ff(x+3*h)/h

(3)

expand(%);

0

(4)

 


 

Download MyRules.mw

@Gillee @acer

 

I realized afterwards that I had forgotten to explain some technical details in my first answer to Gillee.
This omission is corrected in the attached file.

It shows step by step how the exact solution can be obtained by hand without using Maple.


 

restart:

with(Statistics):

# Your problem restated in the correct bayesian form:

# Let X a binomial random variable of parameters N=16 and p.
# p is an unknown value yout want to assess given some outcomes of X.
# The bayesian paradigm then consists in
#   1/ modelling your lack of knowledge about p by saying that p is a realization of some
#      random variable P
#   2/ deciding of some prior distribution Prior(P=q) for P
#   3/ writting the posterior distribution Post(P=q) of P by using Bayes' formula
#
# Thus: Post(P=q | X=K) = Prob(X=K | P=q) * Prior(P=q)
# where the notation Prob(A | B) means "probability of the event A given the event B"
# (you can replace "probability" by "density of probability" in case of continuous random variables)
#
# Now the main result:
#    Let L some likelihood, F the prior distribution of a random variable Y, and G the posterior
#    distribution of Y with respect to L.
#    If F belongs to the family of the conjugate priors of L, then G belonfgs to the same family.
#
# Application:
#    The conjugate prior of the binomial distribution is the family of Beta distributions.
#    Then if you chose Prior(P=q) as a Beta distribution of parameters (a, b), then Post(P=q)
#    will be a Beta distribution of parameters (a', b').
#
# Classical result: Post(P=q | X=K) = Beta(K+a, N-K+b)
#
# How to use this result?
#    It's well known (or not?) that the uniform distribution of support [0, 1] is a Beta
#    distribution of parameters (a=1, b=1).
# Then:
#    Post(P=q | X=K) = Beta(K+1, N-K+1)
#
# With N=16 and K=6 one obtains that
#         the posterior P is a Beta distribution Beta(7, 11)
#

# VERIFICATION (fast acer's code)

randomize():

n_draw      := 10^5:
prior_rate  := Sample(Uniform(0, 1), n_draw):
n_trials    := 16:
dummyV      := Vector(1,datatype=float[8]):
RV          := RandomVariable(Binomial(n_trials,pat)):

subscribers := CodeTools:-Usage( map(proc(u) option hfloat;

                                       global pat;

                                       pat := u;

                                       Sample(RV,dummyV);

                                       dummyV[1];

                                     end proc,

                                     prior_rate) ):


post_rate   := map(i -> if subscribers[i]=6. then prior_rate[i] end if, [$1..n_draw]):
 

memory used=0.66GiB, alloc change=38.01MiB, cpu time=9.69s, real time=9.71s, gc time=267.72ms

 

plots:-display(
   Histogram(post_rate, view=[0..1, default], minbins=100, style='polygon'),
   plot(PDF(BetaDistribution(7, 11), t), t=0..1, color=red, thickness=3)
);

 

 


 

Download FinalAnswer.mw

@Carl Love @acer

 

Hi,
Are the errors catchable byt try..catch..end try the same that are catchable by traperror?
When could it be more interesting to use traperror instead of try..catch..end try?

Hi,
I think you will find some useful answers in the "Posts" section (search for "parallel programming"),in particular here
133632-Parallel-Programming-In-Maple

@hajnayeb 

You want to use a non exact Monte-Carlo Method (MCM) to validate exact theoritical results, is that it?
Seems a little bit strange to me.

So, what do you want exactly: 

  • Assess the mean and variance of X(t) for any t with MCM?
  • Assess the autocotrrelation function of X or its spectral density with MCM?
  • Draw a sample of trajectories X(t, omega) (here omega represents "the alea") for different omega?
  • Do all this stuff in the physical space or in the complex dual space?


Two Maple packages could help you if you want to work with frequency response functions:

  • DynamicSystem
  • Finance (stochastic processes)
  • SignalProcessing

If you want to operate in the physical domain it seems to me  that you have practically all you need in my two previous replies.
OK, the autocorrelation is not computed but you can use the Statistics or SignalProcessing packages to do that and this latter to compute the spectral density.


 

@vv 

I was never directly involved in this kind of competitions, just regularly look at the problems and try to find answers as an amusement, no more than that. I always looked at them as a game and thought rather unfair (again no offense) to use a CAS to find the solution.
But I understand that one can consider as a chalenge to solve some of these problems by a CAS.

I recently discovered video games like Euclidea where you have to solve geometric problems. I was stucked by some of them and finally decided to use Maple to obtain the solution (sometimes successfully). But I always thought I was cheating  because it wasn't me who found the solution but Maple, even if I guided it to do so.

I understood you are a mathematician? So let me ask you this simple question: as a mathematician (not as a Maple user), what solution do you prefer, the one you produced with Maple or the one given here / (and especially the first one)?
 




 

Personnaly I never had any problem to include images in a laTeX file when they were exported from Maple in jpeg or pdf format.
Maybe you could try using these formats instead of the encapsulated postscript... except if you really need eps files for some specific reason?
 

Hi, 
No offense, but I'm always dubitative with this kind of exercise. Those kinds of olympiads you refer to are generally aimed to develop the spirit of intuition and synthesis, the "Ha Ha effect" in some sense, and I using a CAS to solve some problems gives me the impression os using a sledgehammer to kill a fly.
Of course, you may think the opposite and see here as good an opportunity to prove that a CAS can solve problems that only clever reasoning can do?

1 2 3 4 5 6 7 Last Page 1 of 49