> restart; with(Clifford);

_default_Clifford_product;

Clifford:-cmulRS

> M := linalg[matrix](3, 3, [3, 1-'qj'-'qk', -1+'qi', 1+'qj'+'qk', 3, -'qi'-2*'qj'-'qk', -2-'qi', -2+3*'qk', 1+3*'qi']);

M :=
31-qj-qk-1+qi
1+qj+qk3-qi-2qj-qk
-2-qi-2+3qk1+3qi

> B := linalg[diag](1, 1, 1):

> rdet1M = M[1, 1]&q M[2, 2]&q M[3, 3]-M[1, 1]&q M[2, 3]&q M[3, 2])+ M[1, 2]&q M[2, 3]&q M[3, 1]- M[1, 2]&q M[2, 1]&q M[3, 3]+ M[1, 3]&q M[3, 2]&q M[2, 1] - M[1, 3]&q M[3, 1]&q M[2, 2];

Cliplus has been loaded. Definitions for type/climon and type/clipolynom now include &C and &C[K]. Type ?cliprod for help.

rdet1 M = 38 qi - 6 qk - 16 qj

> rdet2M = M[2, 2]&q M[1, 1]&q M[3, 3] - M[2, 2]&q M[1, 3]&q M[3, 1] + M[2, 1]&q M[1, 3]&q M[3, 2]- M[2, 1]&q M[1, 2]&q M[3, 3] + M[2, 3]&q M[3, 1]&q M[1, 2] - M[2, 3]&q M[3, 2] &q M[1, 1];

rdet2 M = 28 qi-6 qk-16 qj

> rdet3M = M[3, 1]&q M[1, 2]&q M[2, 3]- M[3, 1]&q M[1, 3]&q M[2, 2] + M[3, 2]&q M[2, 1]&q M[1, 3] - M[3, 2]&q M[2, 3]&q M[1, 1]+ M[3, 3]&q M[1, 1]&q M[2, 2] - M[3, 3]&q M[1, 2]&q M[2, 1];

rdet3 M = -14+4 qi+8 qk-3qj

> cdet1M = M[3, 3]&q M[2, 2]&q M[1, 1] - M[2, 3]&q M[3, 2]&q M[1, 1] + M[1, 2]&q M[2, 3]&q M[3, 1]- M[2, 2]&q M[1, 3]&q M[3, 1] + M[1, 3]&q M[3, 2]&q M[2, 1] - M[3, 3]&q M[1, 2]&q M[2, 1];

cdet1 M = 38 qi - 6 qk - 16 qj

> cdet2M = M[3, 3]&q M[1, 1]&q M[2, 2] - M[1, 3]&q M[3, 1]&q M[2, 2] + M[2, 3]&q M[3, 1]&q M[1, 2] - M[3, 3]&q M[2, 1]&q M[1, 2] + M[2, 1]&q M[1, 3]&q M[3, 2] - M[1, 1]&q M[2, 3]&q M[3, 2];

cdet2 M = 28 qi - 6 qk - 16 qj

> cdet3M = M[2, 2]&q M[1, 1]&q M[3, 3] - M[1, 2]&q M[2, 1]&q M[3, 3] + M[3, 1]&q M[1, 2]&q M[2, 3] - M[1, 1]&q M[3, 2]&q M[2, 3] + M[3, 2]&q M[2, 1]&q M[1, 3] - M[2, 2]&q M[3, 1]&q M[1, 3];

cdet3 M = 2 qi