The mkisom command finds the matrix of an isometry given the characteristic elements.
For isometries of ℝ2, char will be the angle of rotation for direct isometries or a vector determining the line (through the origin) of reflection for an indirect symmetry.
For isometries of ℝ3, char will be the list consisting of the axis direction and angle of rotation for a direct isometry or a vector normal to the plane of reflection for an indirect isometry.
Examples.
⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ |
⎡ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎦ |
⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ |
⎡ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎦ |
⎡ ⎢ ⎣ |
| ⎤ ⎥ ⎦ |
⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ |