The lll command finds a short basis for the ℤ-modules generated by the rows of a matrix.
Examples.
| ⎡ ⎢ ⎣ |
| ⎤ ⎥ ⎦ | , | ⎡ ⎢ ⎣ |
| ⎤ ⎥ ⎦ | , | ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ | , | ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ |
|
| M := [[3,2,1],[1,2,3],[2,3,1]]:; |
| (S,A,L,O):=lll(M) |
| ⎡ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎦ | , | ⎡ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎦ | , | ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ | , | ⎡ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎦ |
|