sage: A = matrix(ZZ, 2, [1,2, 3,4]); A [1 2] [3 4] sage: Bstar, mu = A.gramm_schmidt()
The rows of the matrix are obtained
from the rows of
by the Gramm-Schmidt procedure.
sage: Bstar [ 1 2] [ 4/5 -2/5] sage: mu [ 0 0] [11/5 0]
A lattice
is a subgroup that
is free of rank
such that
.
For example, the basis
,
for a lattice
is not
LLL reduced because
and
sage: A = matrix(ZZ, 2, [1,2, 3,4]) sage: A.LLL() [1 0] [0 2]
William Stein 2012-09-24