#10347: Implementation of is_(skew_)symmetrizable for matrices
------------------------------+---------------------------------------------
Reporter: stumpc5 | Owner: tbd
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.7.1
Component: combinatorics | Keywords: symmetrizable matrix
Work_issues: | Upstream: N/A
Reviewer: [email protected] | Author: Christian Stump
Merged: | Dependencies:
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Changes (by stumpc5):
* status: needs_work => needs_review
Comment:
Replying to [comment:5 hthomas]:
Hi Hugh,
Thanks for testing the code!
> *
> {{{
> sage: M=matrix([[0,6],[0,0]])
> sage: M.is_symmetrizable(return_diag=true)
> [1, 1]
> }}}
>
> This M is not symmetrizable, and the returned diagonal matrix doesn't
symmetrize it.
The problem here was that the algorithm checks conditions on columns (in
``_travel_column``), but didn't check if an entry `i,j` is zero, that than
`j,i` is zero as well. So the bottom left zero was read, but no check was
made on the top right non-zero...
> *
> {{{
> sage: M=matrix([2])
> sage: M.is_symmetrizable()
> False
> }}}
>
> The code is checking that the diagonal entries are all zero even when
testing for symmetrizability.
I moved this piece of code, so it is only used for skew-symmetrizable
matrices.
> * Zelevinsky spells his name with a final "y".
:-)
Best, Christian
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10347#comment:6>
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