(* wykład IV, strona 59-62 *)

(* klasa1 e, klasa2 c i c.c, klasa 3 b, b.c i b.c.c *)

chi1={1,1,1};

chi2={1,1,-1};

chi3={2,-1,0};

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

c=(({{(1/4), (3/4), 0, 0, 0, ((Sqrt[3])/4)}, {(3/4), (1/4), 0, 0, 0, -((Sqrt[3])/4)}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, -(1/2), ((Sqrt[3])/2), 0}, {0, 0, 0, -((Sqrt[3])/2), -(1/2), 0}, {-((Sqrt[3])/2), ((Sqrt[3])/2), 0, 0, 0, -(1/2)}}));

b=(({{(1/4), (3/4), 0, 0, 0, ((Sqrt[3])/4)}, {(3/4), (1/4), 0, 0, 0, -((Sqrt[3])/4)}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, (1/2), -((Sqrt[3])/2), 0}, {0, 0, 0, -((Sqrt[3])/2), -(1/2), 0}, {((Sqrt[3])/2), -((Sqrt[3])/2), 0, 0, 0, (1/2)}}));

d6dim={Tr[e],Tr[c],Tr[b]};

Solve[d6dim==a1*chi1+a2*chi2+a3*chi3,{a1,a2,a3}]