SetDirectory["~/Factorisation/"];
<<kappaLib.m
<<helper.m

Compute determinants of mediums in Theorem 2.1

Metaclass I:

kappa=emMatrixToKappa[(({{a1, 0, 0, -b1, 0, 0}, {0, a2, 0, 0, -b2, 0}, {0, 0, a3, 0, 0, -b3}, {b1, 0, 0, a1, 0, 0}, {0, b2, 0, 0, a2, 0}, {0, 0, b3, 0, 0, a3}}))];

emDet[kappa]//Simplify

Metaclass II

kappa=emMatrixToKappa[(({{a1, -b1, 0, 0, 0, 0}, {b1, a1, 0, 0, 0, 0}, {0, 0, a2, 0, 0, -b2}, {0, 1, 0, a1, b1, 0}, {1, 0, 0, -b1, a1, 0}, {0, 0, b2, 0, 0, a2}}))];

emDet[kappa]//Simplify

Metaclass IV:

kappa=emMatrixToKappa[(({{a1, 0, 0, -b1, 0, 0}, {0, a2, 0, 0, -b2, 0}, {0, 0, a3, 0, 0, a4}, {b1, 0, 0, a1, 0, 0}, {0, b2, 0, 0, a2, 0}, {0, 0, a4, 0, 0, a3}}))];

emDet[kappa]//Simplify

printNotebook["Determinants.pdf"]