closest_vector() never finishes for a relatively small input #34091
Description
Computation of closest_vector in the following example takes forever.
from sage.modules.free_module_integer import IntegerLattice
L = IntegerLattice( [ (2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
(0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
(0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
(0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
(0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
(0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
(0, -1, 0, 1, -1, -1, 0, 1, 0, 1, 0, 0, 0, 0, 1, -1),
(0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0),
(1, -1, -1, 0, 0, -1, 0, 1, 0, 0, -1, 1, 0, 0, 0, -1),
(1, -1, -1, 0, 0, -1, 0, 1, 0, 0, 1, -1, 0, 0, 0, -1),
(-1, 1, 1, 0, 0, 1, 0, -1, 0, 0, 1, 1, 0, 0, 0, 1),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0),
(0, 1, -1, 0, 1, 0, 0, -1, -1, 0, 0, 1, 0, 1, -1, 0),
(0, 1, -1, 0, 1, 0, 0, -1, 1, 0, 0, 1, 0, 1, -1, 0),
(-1, 0, 1, 0, -1, 0, 1, 1, 0, 0, -1, 0, 1, -1, 0, 0),
(1, 0, -1, 0, 1, 0, 1, -1, 0, 0, 1, 0, -1, 1, 0, 0)
] )
L.closest_vector( (1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0) )
Also, for a bit larger examples (eg., of size 25 x 25) it quickly eats all available memory causing Sage be killed by the system.
CC: @malb
Component: linear algebra
Issue created by migration from https://trac.sagemath.org/ticket/34091