Opened 4 years ago

Last modified 4 years 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:

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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 4 years ago by slelievre

A starting point might be the LLL and BKZ methods of matrices over ZZ:

comment:2 Changed 4 years ago by zimmerma

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.

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