#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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Comment(by wjp):
After discussion at days27, it seems this is an LLL parameter mismatch:
{{{
in gp:
? ??qflll
qflll(x,{flag = 0}):
LLL algorithm applied to the columns of the matrix x. The columns of
x may
be linearly dependent. The result is a unimodular transformation matrix T
such
that x .T is an LLL-reduced basis of the lattice generated by the
column
vectors of x. Note that if x is not of maximal rank T will not be square.
The
LLL parameters are (0.51,0.99), meaning that the Gram-Schmidt
coefficients for
the final basis satisfy mu_{i,j} <= |0.51|, and the Lov\'{a}sz's
constant is
0.99.
}}}
{{{
sage: BB.is_LLL_reduced(eta=.51)
True
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10544#comment:2>
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