5.51.2 Find the matrix of an isometry : mkisom
mkisom takes as argument :

In dimension 3, the list of characteristic elements
(axis direction, angle for a rotation or normal to the plane for
a symmetry) and +1 for a direct isometry or
1 an indirect isometry.
 In dimension 2, a characteristic element (an angle or a vector) and
+1 for a direct isometry (rotation) or 1 for an
indirect isometry (symmetry).
mkisom returns the matrix of the corresponding isometry.
Input :
mkisom([[1,2,1],pi],1)
Output the matrix of the rotation of axis [−1,2,−1] and angle π:
[[2/3,2/3,1/3],[2/3,1/3,2/3],[1/3,2/3,2/3]]
Input :
mkisom([pi],1)
Output the matrix of the symmetry with respect to O :
[[1,0,0],[0,1,0],[0,0,1]]
Input :
mkisom([1,1,1],1)
Output the matrix of the symmetry with respect to the plane x+y+z=0 :
[[1/3,2/3,2/3],[2/3,1/3,2/3],[2/3,2/3,1/3]]
Input :
mkisom([[1,1,1],pi/3],1)
Output the matrix of the product of a rotation of axis [1,1,1] and angle
π/3 and of a symmetry with respect to the plane x+y+z=0:
[[0,1,0],[0,0,1],[1,0,0]]
Input :
mkisom(pi/2,1)
Output the matrix of the plane rotation of angle π/2 :
[[0,1],[1,0]]
Input :
mkisom([1,2],1)
Output matrix of the plane symmetry with respect to the line
of equation x+2y=0:
[[3/5,4/5],[4/5,3/5]]