Find the matrix of an isometry : mkisom

### 2.47.2 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]]`