MACEK: matroid computing  

This project presents a set of tools and routines for reasonably efficient combinatorial computations with representable matroids, especially for matroid constructions and for some structural tests. (If you do not know what a matroid is, then this project is likely not for you.) The program is intended both to help with everyday routines that a matroid-researcher faces (almost) every day, and to allow for long exhausted computations of matroid classes and their properties.

So far, the program deals with matroids represented by matrices over finite fields and partial fields. Many common matroids are distributed with the program, and new ones may be easily entered. An easy manipulation with sets of matroids is supported. One may pivot the matrices, delete or contract elements, and exhaustively generate extensions of matrices. Structural tests for minors, equivalence, branch-width, etc, are also implemented in the project. From version 1.2 also "abstract" tests for representability and for isomorphism are available. (More functions are planned for the future.) Read the complete manual, also in PDF.

The program is freely distributed under the terms of the GNU General Public License as published by the Free Software Foundation. See Copying for details.

Main thanks belong to Geoff Whittle for his motivation, support and encouragement during early Macek development. From the list of other researchers who contributed me helpful ideas and thoughts about practical Macek use I may mention Steven Archer, Sandra Kingan, Xiangqian Zhou, or Paul Wollan.

Copyright (c) 2001--2011 Petr Hlineny.

Not much has happened recently with Macek, besides these new web pages and the online interface...

• The Electronic Journal of Combinatorics: Combinatorial software.
• The EEVL guide.
• Axiom Workshop 2006.
• Sandra Kingan: Oid.

• 2007:    Combinatorial Generation of Matroid Representations: Theory and Practice.
    In: Proceedings of the 3rd Asian Applied Computing Conference, Kathmandu, Nepal, December 10-12, 2005, Advances in Computer Science and Engineering: Reports and Monographs - Vol. 2, Imperial College Press, 2007, 3-7.
• 2006:    Combinatorial Generation of Matroid Representations: Theory and Practice.
    Acta Math. Univ. M. Belii 12 (2005), 31-41.
  URL: actamath.savbb.sk/html/acta12.html.
• 2006:    Equivalence-free exhaustive generation of matroid representations.
    Discrete Appl. Math. 154 (2006), 1210-1222.
  DOI 10.1016/j.dam.2005.12.001. Copyright © Elsevier B.V. Preprint/file.
• 2004:    Using a Computer in Matroid Theory Research.
    Acta Math. Univ. M. Belii 11 (2004), 27-44.
  URL: actamath.savbb.sk/html/acta11.html.
• 2002:    On the Excluded Minors for Matroids of Branch-Width Three.
    Electr. Journal of Combinatorics 9 (2002), www.combinatorics.org, #R32.
  URL: www.combinatorics.org/Volume_9/PDF/v9i1r32.pdf.