#10544: LLL reduced kernel bases are not always correct
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Reporter: rbeezer | Owner: jason, was
Type: defect | Status: new
Priority: major | Milestone: sage-4.6.2
Component: linear algebra | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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On 4.6.1.alpha 3:
{{{
sage: 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: sage: KK=E.right_kernel(LLL=True)
sage: sage: BB=KK.basis_matrix().change_ring(ZZ)
sage: sage: BB.is_LLL_reduced()
False
sage: sage: LL=BB.LLL()
sage: 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]
}}}
I can't say for certain that this is a bug, but it does not look correct
to me. This may happen about one time in twenty for random matrices of
this size. Any smaller and it seemed to be quite rare. Larger and it was
more frequent. Wish I had a better test case to offer.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10544>
Sage <http://www.sagemath.org>
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