#18484: Implement k-chordality of a matroid
------------------------------------+------------------------
       Reporter:  Rudi              |        Owner:
           Type:  enhancement       |       Status:  new
       Priority:  minor             |    Milestone:  sage-6.8
      Component:  matroid theory    |   Resolution:
       Keywords:  chord             |    Merged in:
        Authors:  Travis Scrimshaw  |    Reviewers:
Report Upstream:  N/A               |  Work issues:
         Branch:                    |       Commit:
   Dependencies:                    |     Stopgaps:
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Changes (by {'newvalue': u'Travis Scrimshaw', 'oldvalue': ''}):

 * author:   => Travis Scrimshaw
 * component:  PLEASE CHANGE => matroid theory
 * dependencies:  #18448 =>
 * branch:  u/Rudi/add_test_if_a_matroid_is_ternary =>
 * milestone:  sage-duplicate/invalid/wontfix => sage-6.8
 * keywords:   => chord
 * commit:  3ed9306b5409c351857318d23bd95a8cd3d490f5 =>


Old description:

> There is a straightforward test to see if a matroid is ternary: generate
> the ternary representation local to a basis, and check matroid
> isomorphism. Implement this algorithm. See Matroid.is_binary().

New description:

 A matroid is k-chordal if every circuit `C` of size < k has a ''chord'',
 an element `x` of the ground set is a ''chord'' of `C` if there exists `C
 = A \cup B` such that `A \cup x, B \cup x` are circuits.

--

Comment:

 It's better to not create a new ticket, but instead just push a new
 branch.

 Anyways, I'm going to recycle this ticket for k-chordality of a matroid
 (code to follow shortly, probably tomorrow).

--
Ticket URL: <http://trac.sagemath.org/ticket/18484#comment:6>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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