 
 
 
2.47.1  Recognize an isometry : isom
isom takes as argument the matrix of an linear
application in dimension 2 or 3.
isom returns :
- 
if the linear application is a direct isometry,
 the list of the characteristic elements of this isometry and +1,
- if the linear application is an indirect isometry,
 the list of the characteristic elements of this isometry and -1
- if the linear application is not an isometry,
 [0].
Input :
isom([[0,0,1],[0,1,0],[1,0,0]])
Output :
[[1,0,-1],-1]
which means that this isometry is a 3-d symmetry with respect to the plane 
x − z = 0.
Input :
isom(sqrt(2)/2*[[1,-1],[1,1]])
Output :
[pi/4,1]
Hence, this isometry is a 2-d rotation of angle 
 π/4.
Input :
isom([[0,0,1],[0,1,0],[0,0,1]])
Output :
[0]
therefore this transformation is not an isometry.
 
 
