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Traversing Symmetric Polyhedral Fans

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Mathematical Software – ICMS 2010 (ICMS 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6327))

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Abstract

We propose an algorithm for computing the facets of a pure connected polyhedral fan up to symmetry. The fan is represented by an oracle. With suitable implementations of the oracle the same algorithm can be used for computing secondary fans, Gröbner fans, tropical varieties and Minkowski sums up to symmetry. The algorithm has been implemented in the software Gfan.

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References

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Author information

Authors and Affiliations

  1. Mathematisches Institut, Georg-August-Universität Göttingen, Bunsenstraße 3-5, D-37073, Göttingen, Germany

    Anders Nedergaard Jensen

Authors
  1. Anders Nedergaard Jensen
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Editor information

Editors and Affiliations

  1. Institute for Operations Research and Institute of Theoretical Computer Science, ETH Zurich, 8092, Zurich, Switzerland

    Komei Fukuda

  2. LIX, CNRS, École polytechnique, 91128, Palaiseau cedex, France

    Joris van der Hoeven

  3. Fachbereich Mathematik, TU Darmstadt, 64289, Darmstadt, Germany

    Michael Joswig

  4. Department of Mathematics, Kobe University, 657-8501, Rokko, Kobe, Japan

    Nobuki Takayama

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Jensen, A.N. (2010). Traversing Symmetric Polyhedral Fans. In: Fukuda, K., Hoeven, J.v.d., Joswig, M., Takayama, N. (eds) Mathematical Software – ICMS 2010. ICMS 2010. Lecture Notes in Computer Science, vol 6327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15582-6_47

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  • DOI: https://doi.org/10.1007/978-3-642-15582-6_47

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15581-9

  • Online ISBN: 978-3-642-15582-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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