Opened 9 months ago

Last modified 9 months ago

## #25135 new enhancement

# enumerating short vectors of a lattice

Reported by: | zimmerma | Owned by: | |
---|---|---|---|

Priority: | major | Milestone: | sage-8.2 |

Component: | linear algebra | Keywords: | LLL BKZ |

Cc: | Merged in: | ||

Authors: | Reviewers: | ||

Report Upstream: | N/A | Work issues: | |

Branch: | Commit: | ||

Dependencies: | Stopgaps: |

### Description

in Magma there is a function ShortVectors? to evaluate all vectors of a lattice of norm less than a given bound. It would be nice to have such a function in Sage (I did not find it).

For example in Magma:

> w := RMatrixSpace(IntegerRing(), 2,2) ! [1,2,3,5]; > L:=Lattice(w); > ShortVectors(L,1); [ <(1 0), 1>, <(0 1), 1> ]

### Change History (2)

### comment:1 Changed 9 months ago by

### comment:2 Changed 9 months ago by

thank you, but I opened this ticket precisely because the LLL and BKZ functions (which I put in the keywords by the way) are not sufficient for some applications.

**Note:**See TracTickets for help on using tickets.

A starting point might be the

`LLL`

and`BKZ`

methods of matrices over`ZZ`

: