Begin Step 1:
solradical(Alg3) = [X1, X2, X3, X4]
the radical of Alg3 is re-initialized as `Alg3:1`
End of Step 1
Begin Step 2:
derived algebra( `Alg3:1`) = A1 = [_e1, _e1+_e2, _e2+_e3]
2nd derived algebra( `Alg3:1`) = A2 = []
the factor algebra of `Alg3:1` by the 2nd derived algebra A2 is initialized as `Alg3:2`
projection([_e1, _e2, _e3, _e4]) = [_e5, _e6, _e7, _e8]
_DG([["LieAlgebra", `Alg3:2`, [4]], [[[1, 4, 1], 1], [[2, 4, 1], 1], [[2, 4, 2], 1], [[3, 4, 2], 1], [[3, 4, 3], 1]]])
End of Step 2
Begin Step 3:
hypercenter( `Alg3:2`) = C = []
the factor algebra of `Alg3:2` by the hypercenter C is initialized as `Alg3:3`
projection([_e5, _e6, _e7, _e8]) = [_e9, _e10, _e11, _e12]
_DG([["LieAlgebra", `Alg3:3`, [4]], [[[1, 4, 1], 1], [[2, 4, 1], 1], [[2, 4, 2], 1], [[3, 4, 2], 1], [[3, 4, 3], 1]]])
End of Step 3
Begin Step 4:
derived-algebra(`Alg3:3`) = U = [_e9, _e10, _e11]
complement to U in `Alg3:3` = V = [_e12]
End of Step 4
Begin the Step 5 thru 8 loop, iteration = 1.
Begin Step 5.1:
using the vector X = _e12
f_1 = _z1+1
_z1+1 factors as [[_z1+1, 1]]
f_1 is square-free so go to Step 8.1
End of Step 5.1:
Begin Step 8.1:
the centralizer of _e9 in `Alg3:3` is = M = [_e9, _e10, _e11]
since M = U, the nilradical of `Alg3:3` is U
Begin Step 9:
nilradical(`Alg3:3`) = [_e9, _e10, _e11])
add in the hypercenter C to get nilradical of `Alg3:2`
nilradical(`Alg3:2`) = [_e5, _e6, _e7])
add in the 2nd derived algebra A2 to get nilradical of `Alg3:1`
nilradical(`Alg3:1`) = [_e1, _e2, _e3])
(recall that `Alg3:1` is the nilradical of Alg3)
nilradical(Alg3) = [X1, X2, X3]
End of Step 9:
| (2.11) |