#12208: LU decomposition gives wrong results on cyclotomic matrices (MacOSX-
specific)
------------------------------+---------------------------------------------
Reporter: dimpase | Owner: jason, was
Type: defect | Status: new
Priority: major | Milestone: sage-4.8
Component: linear algebra | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Description changed by dimpase:
Old description:
> create a cyclotomic matrix: (in this case it's even with all integer
> entries)
> {{{
> sage: tgg=SymmetricGroup(5).character_table()
> sage: type(tgg)
> <type 'sage.matrix.matrix_cyclo_dense.Matrix_cyclo_dense'>
> sage: tgg.rank()
> 7
> sage: p,l,u=tgg.LU()
> sage: (l*u).rank()
> 5
> }}}
> indeed, u is wrong:
> {{{
>
> sage: u
> [ 1 -1 1 1 -1 -1 1]
> [ 0 -2 0 1 1 0 -1]
> [ 0 0 1 -1 -1 1 0]
> [ 0 0 0 0 0 0 1]
> [ 0 0 0 0 1 -1 0]
> [ 0 0 0 0 0 0 -1]
> [ 0 0 0 0 0 0 1]
> sage: u.rank()
> 5
> }}}
> Converting tgg into int() works for this particular case, but in general
> this will be not possible.
New description:
On Sage 4.8.alpha4 on MacOSX 10.6 (built from source, patched for flack
nb, but
otherwise pristine)...
create a cyclotomic matrix: (in this case it's even with all integer
entries)
{{{
sage: tgg=SymmetricGroup(5).character_table()
sage: type(tgg)
<type 'sage.matrix.matrix_cyclo_dense.Matrix_cyclo_dense'>
sage: tgg.rank()
7
sage: p,l,u=tgg.LU()
sage: (l*u).rank()
5
}}}
indeed, u is wrong:
{{{
sage: u
[ 1 -1 1 1 -1 -1 1]
[ 0 -2 0 1 1 0 -1]
[ 0 0 1 -1 -1 1 0]
[ 0 0 0 0 0 0 1]
[ 0 0 0 0 1 -1 0]
[ 0 0 0 0 0 0 -1]
[ 0 0 0 0 0 0 1]
sage: u.rank()
5
}}}
Converting tgg into int() works for this particular case, but in general
this will be not possible.
This works on Linux, apparently (e.g. on boxen with Sage 4.7.2), or as
mentioned in the comments.
--
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12208#comment:3>
Sage <http://www.sagemath.org>
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