Advertisement

polymake: a Framework for Analyzing Convex Polytopes

  • Ewgenij Gawrilow
  • Michael Joswig
Part of the DMV Seminar book series (OWS, volume 29)

Abstract

polymake is a software tool designed for the algorithmic treatment of polytopes and polyhedra. We give an overview of the functionality as well as of the structure. This paper can be seen as a first approximation to a polymake handbook.

The tutorial starts with the very basics and ends up with a few polymake applications to research problems. Then we present the main features of the system including the interfaces to other software products. polymake is free software; it is available on the Internet at http://www.math.tu-berlin.de/diskregeom/polymaka/.

Keywords

Convex Hull Rule Base Analyze Convex Positive Orthant Regular Polytopes 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
  2. [2]
    N. AmentaComputational geometry softwareIn Goodman and O’Rourke [19], pp. 951–960.Google Scholar
  3. [3]
    D. Avislrs: A revised implementation of the reverse search vertex enumeration algorithmthis volume, 177–198.Google Scholar
  4. [4]
    D. Avis lrs Version 3.2ftp://mutt.cs.mcgill.ca/pub/C/lrs.html,Oct14 1998
  5. [5]
    D. Avis, D. Bremner, and R. SeidelHow good are convex hull algorithms?Comput. Geom. 7 (1997), no. 5–6, 265–301.MathSciNetzbMATHCrossRefGoogle Scholar
  6. [6]
    D. Avis and K. FukudaA pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra.Discrete Comput. Geom. 8 (1992), no. 3, 295–313.MathSciNetGoogle Scholar
  7. [7]
    M.M. Bayer and C.W. LeeCombinatorial aspects of convex polytopespp. 485–534, In Gruber and Wills [20], 1993.Google Scholar
  8. [8]
    G. Blind and R. BlindConvex polytopes without triangular facesIsrael J. Math. 71 (1990), no. 2, 129–134.MathSciNetzbMATHGoogle Scholar
  9. [9]
    G. Blind and R. Blind Cubical 4-polytopes with few verticesGeom. Dedicata 66 (1997), no. 2, 223–231.MathSciNetCrossRefGoogle Scholar
  10. [10]
    D. Bremner PolytopeBase Version 0.2 http://www.math.Washington.edu/“bremner/PolytopeBase Mar 4, 1999.
  11. [11]
    T. Christof and A. Loebel PORTA: POlyhedron Representation Transformation Algorithm, Version 1.3.2, http://www.iwr.uni-heidelberg.de/iwr/comopt/soft Nov 24, 1998.
  12. [12]
    T.H. Cormen, C.E. Leiserson, and R.L. RivestIntroduction to algorithmsMIT Press, 1990.Google Scholar
  13. [13]
    H.S.M. CoxeterRegular polytopesDover, 1973.Google Scholar
  14. [14]
    H. EdelsbrunnerAlgorithms in combinatorial geometrySpringer, 1987.Google Scholar
  15. [15]
    C.Young et alPOV-Ray: Persistence Of Vision, Version 3.1, http://www.povray.org, 1999.
  16. [16]
    F.J. Brandenburg et al Graphlet, Version 5.0, http://www.fmi.uni-passau.de/Graphlet Jan 11, 1999.
  17. [17]
    K. Fukuda cddplus, Version 0.76a, http://www.ifor.math.ethz.ch Jun 8,1999.
  18. [18]
    K. Fukuda and A. ProdonDouble description method revisitedLNCS, vol. 1120, 1996.Google Scholar
  19. [19]
    J.E. Goodman and J. O’Rourke (eds.)Handbook of discrete and computational geometryCRC Press, 1997.Google Scholar
  20. [20]
    P.M. Gruber and J.M. Wills (eds.)Handbook of convex geometryNorth-Holland, 1993.Google Scholar
  21. [21]
    J.E. HumphreysReflection groups and Coxeter groupsCambridge Univ. Press, 1992, corrected paper-back ed.zbMATHGoogle Scholar
  22. [22]
    M. JoswigReconstructing a non-simple polytope from its graphthis Volume, 167–176.Google Scholar
  23. [23]
    M. Joswig and G.M. ZieglerNeighborly cubical polytopesDiscrete Comput. Geometry (to appear), math.CO/9812033.Google Scholar
  24. [24]
    G. KalaiLinear programming the simplex algorithm and simple polytopesMath. Program. Ser. B 79 (1997), 217–233.Google Scholar
  25. [25]
    D.E. KnuthThe art of computer programming I. Fundamental algorithms3rd ed., Addison-Wesley, 1997.Google Scholar
  26. [26]
    D.E. Knuth The art of computer programming III. Sorting and searching 2nd ed., Addison-Wesley, 1997.Google Scholar
  27. [27]
    S. Levy, T. Münzner, and M. Phillips, Geomview, Version 1.6.1, http://www.geom.umn.edu/software/geomview/Oct 30, 1997.
  28. [28]
    D.R. Musser and A. SainiSTL tutorial and reference guideAddison-Wesley, 1996.Google Scholar
  29. [29]
    J. Rambau TOPCOM, Version 0.2.0, http://www.zib.de/rambau/topcom.html Jul 28,1999.
  30. [30]
    J. Richter-Gebert and U.H. KortenkampThe interactive geometry software CinderellaSpringer, 1999.Google Scholar
  31. [31]
    B. StroustrupThe C++ programming languageAddison-Wesley, 1997, 3rd ed.Google Scholar
  32. [32]
    L. Wall, T. Christiansen, and R.L. SchwartzProgramming PerlO’Reilly, 1996, 2nd ed.Google Scholar
  33. [33]
    G.M. ZieglerLectures on polytopesSpringer, 1998, 2nd ed.Google Scholar

Copyright information

© Springer Basel AG 2000

Authors and Affiliations

  • Ewgenij Gawrilow
    • 1
  • Michael Joswig
    • 1
  1. 1.Fachbereich Mathematik, MA 7-1Technische Universität BerlinBerlinGermany

Personalised recommendations