polyTop: Software for Computing Topology of Smooth Real Surfaces

  • Danielle A. Brake
  • Jonathan D. Hauenstein
  • Margaret H. ReganEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10931)


A common computational problem is to compute topological information about a real surface defined by a system of polynomial equations. Our software, called polyTop, leverages numerical algebraic geometry computations from Bertini and Bertini_real with topological computations in javaPlex to compute the Euler characteristic, genus, Betti numbers, and generators of the fundamental group of a smooth real surface. Several examples are used to demonstrate this new software.


Numerical algebraic geometry Topology Cell decomposition Graphs Euler characteristic Betti numbers Fundamental group 



The authors thank Mikael Vejdemo-Johansson for input regarding javaPlex. All authors acknowledge support from NSF ACI-1440607/1460032. Additional support for JDH was provided by Sloan Research Fellowship BR2014-110 TR14 and for MHR by Schmitt Leadership Fellowship in Science and Engineering.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Danielle A. Brake
    • 1
  • Jonathan D. Hauenstein
    • 2
  • Margaret H. Regan
    • 2
    Email author
  1. 1.Department of MathematicsUniversity of Wisconsin-Eau ClaireEau ClaireUSA
  2. 2.Department of Applied and Computational Mathematics and StatisticsUniversity of Notre DameNotre DameUSA

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