Obtaining a right kernel of an integer matrix and requesting an LLL-
reduced independent set, would appear to return something just shy of
being LLL-reduced. But maybe it is a question of different parameters
used in the creation versus the check, or something else. I know what
it means to be LLL-reduced, but not enough to say if the following is
a bug.
This doesn't happen often (one time in 30 for 5x8 matrices) and not
often enough for smaller random matrices, so I don't have a better
example.
I'll file a ticket with slightly better info if there isn't a rational
explanation of this behavior (or even an integral explanation). And
it looks like the basis_matrix() is over the rationals, which I
wouldn't expect either.
{{{
sage: E=matrix(ZZ, 5, 8,
[5, -23, 21, 77, -50, 8, -76, 16, 2,
-9, 8, 30, -19, 3, -29, 6, 4, -16, 13,
53, -30, 4, -47, 9, 0, 5, -14, -24,
33, -5, 47, -14, -2, 11, -9, -35, 23,
-5, 34, -7])
sage: KK=E.right_kernel(LLL=True)
sage: BB=KK.basis_matrix().change_ring(ZZ)
sage: BB.is_LLL_reduced()
False
sage: LL=BB.LLL()
sage: LL-BB
[0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0]
[1 0 1 0 1 1 0 1]
[0 0 0 0 0 0 0 0]
}}}
--
To post to this group, send an email to [email protected]
To unsubscribe from this group, send an email to
[email protected]
For more options, visit this group at http://groups.google.com/group/sage-devel
URL: http://www.sagemath.org
