Implementation of is_(skew_)symmetrizable for matrices

[stumpc5]

matrices are lacking methods for testing (skew-)symmetrizability. Those methods are needed for the cluster algebra and quiver package, see Ticket #10298.

CC: @saliola @hughrthomas

Component: combinatorics

Keywords: symmetrizable matrix

Author: Christian Stump

Reviewer: Hugh Thomas

Merged: sage-5.0.beta5

Issue created by migration from https://trac.sagemath.org/ticket/10347

[stumpc5]

comment:2

Apply only trac_10347_is_skew_symmetrizable-cs.patch

[fchapoton]

comment:3

You should modify the header of your patch : add something like

#10347 Implementation of is_(skew_)symmetrizable for matrices

Then the buildbot will be more happy.

[stumpc5]

comment:4

Replying to @fchapoton:

Then the buildbot will be more happy.

done, thanks.

[hughrthomas]

comment:5

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.

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.

• Zelevinsky spells his name with a final "y".

[hughrthomas]

Reviewer: hthomas@unb.ca

[stumpc5]

comment:6

Replying to @hughrthomas:

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