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Recognize an isometry : isom

isom takes as argument the matrix of an linear application in dimension 2 or 3.
isom returns : Input :
Output :
which means that this isometry is a 3-d symmetry with respect to the plane x  -  z  =   0.
Input :
Output :
Hence, this isometry is a 2-d rotation of angle $\displaystyle {\frac{{\pi}}{{4}}}$.
Input :
Output :
therefore this transformation is not an isometry.

giac documentation written by Renée De Graeve and Bernard Parisse