a = [1, 2, 3; 4, 5, 6; 7, 8, 9; 10, 11, 12];

l0 = [1, 0, 0; 4, 5, 0; 7, 8, 9; 10, 11, 12];
l1 = [1, 2, 0; 4, 5, 6; 7, 8, 9; 10, 11, 12];
l2 = [1, 2, 3; 4, 5, 6; 7, 8, 9; 10, 11, 12];
lm1 = [0, 0, 0; 4, 0, 0; 7, 8, 0; 10, 11, 12];
lm2 = [0, 0, 0; 0, 0, 0; 7, 0, 0; 10, 11, 0];
lm3 = [0, 0, 0; 0, 0, 0; 0, 0, 0; 10, 0, 0];
lm4 = [0, 0, 0; 0, 0, 0; 0, 0, 0; 0, 0, 0];

(tril (a, -4) == lm4 && tril (a, -3) == lm3
 && tril (a, -2) == lm2 && tril (a, -1) == lm1
 && tril (a) == l0 && tril (a, 1) == l1 && tril (a, 2) == l2)
