SetDirectory["/www/user/fdahl/papers/Conjugation/"];
<<kappaLib.m
<<Petrov.m

Class I: (1bar(1) 1bar(1) 1bar(1))

B=(({{0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}}));

V=(({{ sigma1, tau1, 0, 0, 0, 0}, {-tau1, sigma1, 0, 0, 0, 0}, {0, 0, sigma2, tau2, 0, 0}, {0, 0, -tau2, sigma2, 0, 0}, {0, 0, 0, 0,  sigma3, tau3}, {0, 0, 0, 0, -tau3,  sigma3}}));

Eigenvalues[V]

mathcal(W) contains only one element:

W=(({{0, 1, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 1, 0}}));
(* Check that W has signature (+++---)*)
Eigenvalues[W]

S=Sqrt[2]B.(({{(1/(Sqrt[2])), 0, 0, 0, 0, 0}, {0, 0, (1/(Sqrt[2])), 0, 0, 0}, {0, 0, 0, 0, (1/(Sqrt[2])), 0}, {0, (1/(Sqrt[2])), 0, 0, 0, 0}, {0, 0, 0, (1/(Sqrt[2])), 0, 0}, {0, 0, 0, 0, 0, (1/(Sqrt[2]))}}));

Check that S is in set mathcal(S)

Transpose[S].B.S==W

Compute result

res=S.V.Inverse[S];
res//MatrixForm

Petrov[res]

Export notebook as .pdf

NotebookPrint[SelectedNotebook[],"/www/user/fdahl/papers/Conjugation/notebooks/ClassI.pdf"]