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#
# i.m -- invariante
#
# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
#
A0 = [
2, 1, 0, 0;
0, 2, 1, 0;
0, 0, 2, 0;
0, 0, 0, 3
];
# find a 3x3 matrix in SL(3,Z)
function retval = zufallswert()
x = round(rand() * 10) - 2;
if (x >= 0)
x = x + 1;
endif
retval = x;
end
function retval = zufallsmatrix(n)
retval = zeros(n, n);
for i = (1:n)
for j = (1:n)
retval(i,j) = zufallswert();
end
end
end
function retval = regulaer(n)
d = 0;
do
retval = zufallsmatrix(2);
d = det(retval);
until (d == 1);
end
function retval = eingebettet(n,k)
retval = eye(n);
retval(k:k+1,k:k+1) = regulaer(2);
end
format long
B = eye(4);
B = B * eingebettet(4,3)
B = B * eingebettet(4,1)
B = B * inverse(eingebettet(4,2))
#B = B * eingebettet(4,2)
B
inverse(B)
A = round(B * A0 * inverse(B))
D = A - 2 * eye(4)
rank(D)
E = round(D*D*D*D)
rank(E')
rref(E)
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