#12208: LU decomposition gives wrong results on cyclotomic matrices (MacOSX-
specific)
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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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Comment(by rbeezer):
Replying to [comment:5 dimpase]:
> Replying to [comment:4 rbeezer]:
> > {{{pivot='partial'}}} would basically bypass a call to {{{abs()}}}
> {{{pivot='partial'}}} gives the wrong result, while
{{{pivot='nonzero'}}} computes the things correctly.
OK, I had it backwards (it was late!) and your results I think might point
out the root cause.
It looks to me like the {{{abs()}}} of a number field elements are MPFR
real numbers. So while searching for a "largest" element in a column,
there may be some zero/nonzero confusion?
Perhaps we should check that the return value of the absolute value
function lives in the fraction field of the base ring before allowing
partial pivoting? In other words, we need an exact result to proceed.
The implementation is really only designed for this case. Does that sound
like a reasonable solution to you?
Or maybe there is a better function to be using for the "magnitude" of an
element of an arbitrary ring/field? Maybe a question for sage-devel - I
can't think of the answer.
Rob
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12208#comment:6>
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