#12208: LU decomposition gives wrong results on cyclotomic matrices
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Reporter: dimpase | Owner: jason, was
Type: PLEASE CHANGE | 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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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.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12208>
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