> restart; with(Clifford);

_default_Clifford_product;

Clifford:-cmulRS

> M := linalg[matrix] (4, 4, [2, 'qk', 'qi', 0, -'qk', 1, 0, 'qi', -'qi', 0, 3, 'qk', 0, -'qi', -'qk', 4]);

M :=
2qkqi0
-qk10qi
-qi03qk
0-qi-qk4

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

> rdet1M= M[1, 1]&q M[2, 2]&q M[3, 3]&qM[4, 4]-M[1, 1]&q M[2, 3]&q M[3, 2] &q M[4, 4]-M[1, 1]&q M[2, 2] &q M[3, 4]&q M[4, 3] +M[1, 1]&q M[2, 3]&q M[3, 4]&q M[4, 2] + M[1, 1]&q M[2, 4]&q M[4, 3]&q M[3, 2] -M[1, 1]&q M[2, 4]&q M[4, 2]&q M[3, 3] + M[1, 2]&q M[2, 1]&q M[3, 4]&q M[4, 3] - M[1, 2]&q M[2, 1]&q M[3, 3]&q M[4, 4] + M[1, 2]&q M[2, 3] &q M[3, 1] &q M[4, 4] - M[1, 2]&q M[2, 3]&q M[3, 4]&q M[4, 1] + M[1, 2]&q M[2, 4] &q M[4, 1]&q M[3, 3] - M[1, 2] &q M[2, 4]&q M[4, 3]&q M[3, 1] + M[1, 3]&q M[3, 2]&q M[2, 1]&q M[4, 4] - M[1, 3]&q M[3, 2]&q M[2, 4]&q M[4, 1] + M[1, 3] &q M[3, 1]&q M[2, 4] &q M[4, 2] - M[1, 3]&q M[3, 1] &q M[2, 2] &q M[4, 4]+ M[1, 3] &q M[3, 4]&q M[4, 1]&q M[2, 2]- M[1, 3]&q M[3, 4]&q M[4, 2]&q M[2, 1] + M[1, 4] &q M[4, 2] &q M[2, 1] &q M[3, 3]- M[1, 4]&q M[4, 2]&q M[2, 3]&q M[3, 1])+ M[1, 4]&q M[4, 1]&q M[2, 3]&q M[3, 2] - M[1, 4]&q M[4, 1]&q M[2, 2]&q M[3, 3] + M[1, 4] &q M[4, 3] &q M[3, 1] &q M[2, 2]- M[1, 4]&q M[4, 3] &q M[3, 2] &q M[2, 1];

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

rdet1 M = 4

> rdet2M = M[2, 2]&q M[1, 1]&q M[3, 3]&q M[4, 4]- M[2, 3]&q M[3, 2] &q M[1, 1]&q M[4, 4]- M[2, 2] &q M[1, 1]&q M[3, 4]&q M[4, 3] + M[2, 3]&q M[3, 4]&q M[4, 2] &q M[1, 1]+ M[2, 4]&q M[4, 3]&q M[3, 2] &q M[1, 1] -M[2, 4]&q M[4, 2]&q M[1, 1]&q M[3, 3] + M[2, 1]&q M[1, 2]&q M[3, 4]&q M[4, 3] -M[2, 1]&q M[1, 2]&q M[3, 3]&q M[4, 4] + M[2, 3] &q M[3, 1] &q M[1, 2]&q M[4, 4] -M[2, 3]&q M[3, 4]&q M[4, 1] &q M[1, 2] + M[2, 4] &q M[4, 1]&q M[1, 2] &q M[3, 3] -M[2, 4]&q M[4, 3]&q M[3, 1] &q M[1, 2] + M[2, 1] &q M[1, 3]&q M[3, 2]&q M[4, 4] - M[2, 4]&q M[4, 1] &q M[1, 3]&q M[3, 2] + M[2, 4] &q M[4, 2] &q M[1, 3] &q M[3, 1] - M[2, 2] &q M[1, 3]&q M[3, 1] &q M[4, 4]+ M[2, 2] &q M[1, 3] &q M[3, 4]&q M[4, 1]- M[2, 1]&q M[1, 3]&q M[3, 4]&q M[4, 2] + M[2, 1] &q M[1, 4] &q M[4, 2] &q M[3, 3]- M[2, 3]&q M[3, 1]&q M[1, 4]&q M[4, 2]+ M[2, 3]&q M[3, 2]&qM[1, 4]&q M[4, 1] -M[2, 2]&q M[3, 3] &q M[1, 4]&q M[4, 1]+ M[2, 2] &q M[1, 4] &q M[4, 3] &q M[3, 1]- M[2, 1] &q M[1, 4]&q M[4, 3] &q M[3, 2];

rdet2 M = 4

> rdet3M = M[3, 3]&q M[1, 1]&q M[2, 2]&q M[4, 4]- M[3, 2] &q M[2, 3]&q M[1, 1]&q M[4, 4]-M[3, 4]&q M[4, 3] &q M[1, 1]&q M[2, 2] + M[3, 4]&q M[4, 2] &q M[2, 3]&q M[1, 1]+ M[3, 2] &q M[2, 4]&q M[4, 3]&q M[1, 1] -M[3, 3] &q M[1, 1]&q M[2, 4]&q M[4, 2]+ M[3, 4]&q M[4, 3] &q M[2, 1]&q M[1, 2] -M[3, 3] &q M[2, 1]&q M[1, 2]&q M[4, 4] + M[3, 1] &q M[1, 2]&q M[2, 3] &q M[4, 4] -M[3, 4]&q M[4, 1] &q M[1, 2] &q M[2, 3] + M[3, 3] &q M[1, 2] &q M[2, 4] &q M[4, 1] - M[3, 1] &q M[1, 2] &q M[2, 4]&q M[4, 3]+ M[3, 2]&q M[2, 1] &q M[1, 3]&q M[4, 4] - M[3, 2] &q M[2, 4]&q M[4, 1] &q M[1, 3] + M[3, 1] &q M[1, 3] &q M[2, 4] &q M[4, 2] - M[3, 1] &q M[1, 3]&q M[2, 2] &qM[4, 4]+ M[3, 4] &q M[4, 1] &q M[1, 3] &q M[2, 2] - M[3, 4]&q M[4, 2] &q M[2, 1]&q M[1, 3] + M[3, 3] &q M[1, 4] &q M[4, 2] &q M[2, 1]- M[3, 1]&q M[1, 4]&q M[4, 2] &q M[2, 3]+ M[3, 2] &q M[2, 3] &q M[1, 4]&q M[4, 1] -M[3, 3] &q M[1, 4]&q M[4, 1] &q M[2, 2]+ M[3, 1] &q M[1, 4] &q M[4, 3] &q M[2, 2]- M[3, 2] &q M[2, 1] &q M[1, 4]&q M[4, 3];

rdet3 M = 4

> rdet4M = M[4, 4] &q M[1, 1]&q M[2, 2]&q M[3, 3]- M[4, 4]&q M[1, 1] &q M[2, 3]&q M[3, 2]-M[4, 3] &q M[3, 4]&q M[1, 1]&q M[2, 2] + M[4, 2] &q M[2, 3]&q M[3, 4]&q M[1, 1]+ M[4, 3]&q M[3, 2] &q M[2, 4]&q M[1, 1] -M[4, 2]&q M[2, 4] &q M[1, 1]&q M[3, 3]+ M[4, 3] &q M[3, 4]&q M[1, 2] &q M[2, 1] -M[4, 4] M[1, 2] &q &q M[2, 1]&q M[3, 3] + M[4, 4] &q M[1, 2]&q M[2, 3] &q M[3, 1] -M[4, 1] &q M[1, 2] &q M[2, 3] &q M[3, 4] + M[4, 1] &q M[1, 2] &q M[2, 4] &q M[3, 3]- M[4, 3] &q M[3, 1] &q M[1, 2] &q M[2, 4]+ M[4, 4] &q M[1, 3]&q M[3, 2]&q M[2, 1] -M[4, 1] &q M[1, 3]&q M[3, 2] &q M[2, 4] + M[4, 2] &q M[2, 4] &q M[1, 3] &q M[3, 1] - M[4, 4]&q M[1, 3] &q M[3, 1] &q M[2, 2]+ M[4, 1] &q M[1, 3] &q M[3, 4] &q M[2, 2] -M[4, 2] &q M[2, 1]&q M[1, 3]&q M[3, 4] + M[4, 2] &q M[2, 1] &q M[1, 4] &q M[3, 3]- M[4, 2] &q M[2, 3]&q M[3, 1]&q M[1, 4]+ M[4, 1] &q M[1, 4] &q M[2, 3] &q M[3, 2] -M[4, 1]&q M[1, 4] &q M[2, 2] &q M[3, 3] + M[4, 3] &q M[3, 1] &q M[1, 4] &q M[2, 2]- M[4, 3] &q M[3, 2] &q M[2, 1] &q M[1, 4];

rdet4 M = 4

> cdet1M = M[4, 4] &q M[3, 3]&q M[2, 2]&q M[1, 1]- M[4, 4]&q M[2, 3] &q M[3, 2] &q M[1, 1]-M[3, 4]&q M[4, 3] &q M[2, 2] &q M[1, 1] + M[2, 3]&q M[3, 4]&q M[4, 2] &q M[1, 1]+ M[2, 4]&q M[4, 3]&q M[3, 2] &q M[1, 1] -M[3, 3] &q M[2, 4]&q M[4, 2] &q M[1, 1]+ M[3, 4] &q M[4, 3] &q M[1, 2]&q M[2, 1] -M[4, 4] &q M[3, 3] &q M[1, 2]&q M[2, 1] + M[4, 4] &q M[1, 2]&q M[2, 3] &q M[3, 1] -M[1, 2] &q M[2, 3] &q M[3, 4]&q M[4, 1] + M[3, 3] &q M[1, 2] &q M[2, 4] &q M[4, 1]-M[1, 2] &q M[2, 4] &q M[4, 3] &q M[3, 1]+ M[4, 4] &q M[1, 3]&q M[3, 2]&q M[2, 1] - M[1, 3]&q M[3, 2] &q M[2, 4] &q M[4, 1] + M[2, 4] &q M[4, 2]&q M[1, 3] &q M[3, 1] -M[4, 4] &q M[2, 2] &q M[1, 3]&q M[3, 1] + M[2, 2] &q M[1, 3] &q M[3, 4] &q M[4, 1] -M[1, 3]&q M[3, 4] &q M[4, 2] &q M[2, 1] + M[3, 3] &q M[1, 4] &q M[4, 2] &q M[2, 1]-M[1, 4] &q M[4, 2] &q M[2, 3]&q M[3, 1]+M[2, 3] &q M[3, 2] &q M[1, 4] &q M[4, 1] - M[3, 3] &q M[2, 2] &q M[1, 4]&q M[4, 1] +M[2, 2] &q M[1, 4] &q M[4, 3] &q M[3, 1] - M[1, 4] &q M[4, 3] &q M[3, 2] &q M[2, 1];

cdet1 M = 4

> cdet2M = M[4, 4] &q M[3, 3]&q M[1, 1]&q M[2, 2]- M[4, 4] &q M[1, 1]&q M[2, 3] &q M[3, 2]-M[3, 4]&q M[4, 3] &q M[1, 1] &q M[2, 2] +M[1, 1] &q M[2, 3]&q M[3, 4]&q M[4, 2]+ M[1, 1] &q M[2, 4]&q M[4, 3]&q M[3, 2] -M[3, 3] &q M[1, 1] &q M[2, 4]&q M[4, 2]+ M[3, 4] &q M[4, 3]&q M[2, 1] &q M[1, 2] -M[4, 4] &q M[3, 3]&q M[2, 1] &q M[1, 2] + M[4, 4]&q M[2, 3] &q M[3, 1] &q M[1, 2] -M[2, 3] &q M[3, 4]&q M[4, 1] &q M[1, 2] + M[3, 3] &q M[2, 4] &q M[4, 1] &q M[1, 2]- M[2, 4] &q M[4, 3] &q M[3, 1]&q M[1, 2] + M[4, 4]&q M[2, 1] &q M[1, 3]&q M[3, 2] - M[2, 4] &q M[4, 1] &q M[1, 3]&q M[3, 2] +M[1, 3] &q M[3, 1] &q M[2, 4] &q M[4, 2] -M[4, 4] &q M[1, 3]&q M[3, 1] &q M[2, 2] + M[1, 3] &q M[3, 4] &q M[4, 1] &q M[2, 2] -M[2, 1] &q M[1, 3]&q M[3, 4]&q M[4, 2] + M[3, 3] &q M[2, 1] &q M[1, 4] &q M[4, 2]-M[2, 3]&q M[3, 1] &q M[1, 4] &q M[4, 2]+ M[1, 4] &q M[4, 1] &q M[2, 3] &q M[3, 2] - M[3, 3] &q M[1, 4]&q M[4, 1] &q M[2, 2] + M[1, 4] &q M[4, 3] &q M[3, 1] &q M[2, 2]-M[2, 1] &q M[1, 4] &q M[4, 3] &q M[3, 2];

cdet2 M = 4

> cdet3M = M[4, 4]&q M[2, 2]&q M[1, 1] &q M[3, 3]- M[4, 4]&q M[1, 1] &q M[3, 2] &q M[2, 3]-M[2, 2] &q M[1, 1] &q M[3, 4]&q M[4, 3] +M[1, 1] &q M[3, 4]&q M[4, 2] &q M[2, 3]+ M[1, 1] &q M[3, 2] &q M[2, 4]&q M[4, 3] -M[2, 4]&q M[4, 2] &q M[1, 1] &q M[3, 3]+ M[1, 2]&q M[2, 1] &q M[3, 4] &q M[4, 3] -M[4, 4] &q M[1, 2]&q M[2, 1] &q M[3, 3] + M[4, 4] &q M[3, 1] &q M[1, 2]&q M[2, 3] - M[3, 4]&q M[4, 1] &q M[1, 2] &q M[2, 3] +M[1, 2] &q M[2, 4] &q M[4, 1] &q M[3, 3] -M[3, 1] &q M[1, 2] &q M[2, 4] &q M[4, 3]+ M[4, 4]&q M[3, 2]&q M[2, 1] &q M[1, 3] -M[3, 2] &q M[2, 4] &q M[4, 1] &q M[1, 3] + M[2, 4] &q M[4, 2] &q M[3, 1] &q M[1, 3] -M[4, 4] &q M[2, 2]&q M[3, 1] &q M[1, 3] + M[2, 2] &q M[3, 4] &q M[4, 1] &q M[1, 3] -M[3, 4] &q M[4, 2] &q M[2, 1] &q M[1, 3] + M[1, 4] &q M[4, 2] &q M[2, 1] &q M[3, 3]-M[3, 1] &q M[1, 4] &q M[4, 2] &q M[2, 3]+ M[1, 4] &q M[4, 1] &q M[3, 2] &q M[2, 3] - M[2, 2] &q M[1, 4]&q M[4, 1] &q M[3, 3]+M[2, 2] &q M[3, 1] &q M[1, 4] &q M[4, 3] - M[3, 2] &q M[2, 1] &q M[1, 4] &q M[4, 3];

cdet3 M = 4

> cdet4M = M[3, 3]&q M[2, 2]&q M[1, 1] &q M[4, 4]-M[2, 3] &q M[3, 2] &q M[1, 1] &q M[4, 4]-M[2, 2] &q M[1, 1] &q M[4, 3] &q M[3, 4] + M[1, 1] &q M[4, 2] &q M[2, 3]&q M[3, 4]+ M[1, 1] &q M[4, 3]&q M[3, 2] &q M[2, 4] -M[3, 3] &q M[1, 1] &q M[4, 2] &q M[2, 4]+ M[1, 2]&q M[2, 1] &q M[4, 3] &q M[3, 4] -M[3, 3] &q M[1, 2]&q M[2, 1] &q M[4, 4] + M[1, 2]&q M[2, 3] &q M[3, 1] &q M[4, 4] -M[4, 1] &q M[1, 2] &q M[2, 3] &q M[3, 4] + M[3, 3] &q M[4, 1] &q M[1, 2] &q M[2, 4]- M[4, 3] &q M[3, 1] &q M[1, 2] &q M[2, 4]+ M[1, 3]&q M[3, 2]&q M[2, 1] &q M[4, 4] - M[4, 1] &q M[1, 3]&q M[3, 2] &q M[2, 4] + M[1, 3] &q M[3, 1] &q M[4, 2] &q M[2, 4] -M[2, 2] &q M[1, 3]&q M[3, 1] &q M[4, 4] + M[2, 2] &q M[4, 1] &q M[1, 3] &q M[3, 4] -M[4, 2] &q M[2, 1] &q M[1, 3]&q M[3, 4] + M[3, 3] &q M[4, 2] &q M[2, 1] &q M[1, 4]-M[4, 2] &q M[2, 3]&q M[3, 1] &q M[1, 4]+M[2, 3] &q M[3, 2] &q M[4, 1] &q M[1, 4] - M[3, 3] &q M[2, 2]&q M[4, 1] &q M[1, 4] +M[2, 2] &q M[4, 3] &q M[3, 1] &q M[1, 4] -M[4, 3] &q M[3, 2] &q M[2, 1] &q M[1, 4];

cdet4 M = 4