Wyznacznik macierzy

1145 days ago by mnbvmar

a,b,c,d = var('a'), var('b'), var('c'), var('d') a = sqrt(1-b^2-c^2-d^2) M = matrix(SR, 3, 3, [[1-2*c^2-2*d^2, 2*(a*c+b*d), 2*(b*c-a*d)], [2*(b*d-a*c), 1-2*b^2-2*c^2, 2*(a*b+c*d)], [2*(a*d+b*c), 2*(c*d-a*b), 1-2*b^2-2*d^2]]) 
       
       
[                    -2*c^2 - 2*d^2 + 1 2*b*d + 2*sqrt(-b^2 - c^2 -
d^2 + 1)*c 2*b*c - 2*sqrt(-b^2 - c^2 - d^2 + 1)*d]
[2*b*d - 2*sqrt(-b^2 - c^2 - d^2 + 1)*c                     -2*b^2 -
2*c^2 + 1 2*c*d + 2*sqrt(-b^2 - c^2 - d^2 + 1)*b]
[2*b*c + 2*sqrt(-b^2 - c^2 - d^2 + 1)*d 2*c*d - 2*sqrt(-b^2 - c^2 -
d^2 + 1)*b                     -2*b^2 - 2*d^2 + 1]
f = M.determinant() g = f.expand() g.simplify() 
       
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