#18910: Boost minimum spanning tree
-------------------------------------+-------------------------------------
       Reporter:  borassi            |        Owner:
           Type:  enhancement        |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-6.8
      Component:  graph theory       |   Resolution:
       Keywords:  Boost, minimum     |    Merged in:
  spanning tree                      |    Reviewers:
        Authors:  Michele Borassi    |  Work issues:
Report Upstream:  N/A                |       Commit:
         Branch:                     |  4bbb2980aab4b0a81fc07cf62afa5395ee7719c1
  u/borassi/boost_minimum_spanning_tree|     Stopgaps:
   Dependencies:  #18876, #18906     |
-------------------------------------+-------------------------------------

Comment (by Rudi):

 Replying to [comment:14 ncohen]:
 > Stefan, Rudi? Does it look okay to you if by changing the behaviour of a
 graph spanning tree routine, the output of
 > {{{
 > sage: Z = lift_cross_ratios(A, to_sixth_root_of_unity)
 > }}}
 >
 > at line 416 of matroids/utilities.py changes like that?
 > {{{
 > Failed example:
 >     Z
 > Expected:
 >     [ 1  0  1  1  1]
 >     [ 1  1  0  0  z]
 >     [ 0  1 -z -1  0]
 > Got:
 >     [     1      0      1      1      1]
 >     [     1      1      0      0      z]
 >     [     0  z - 1      1 -z + 1      0]
 > }}}
 >
 > It may be caused by a different spanning tree, or by a reordering of its
 edges.

 Yes, that looks OK. This output matrix Z is fixed up to scaling of rows
 and columns, and the tree is used to determine the scaling. Looks like in
 this example the bottom row is scaled by  z-1 (which happens to equal
 -z^-1^ in that ring, z is is a sixth root of unity).

 So it's safe to just update the output of the test.

--
Ticket URL: <http://trac.sagemath.org/ticket/18910#comment:15>
Sage <http://www.sagemath.org>
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