×

Traversing symmetric polyhedral fans. (English) Zbl 1294.68157

Fukuda, Komei (ed.) et al., Mathematical software – ICMS 2010. Third international congress on mathematical software, Kobe, Japan, September 13–17, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-15581-9/pbk). Lecture Notes in Computer Science 6327, 282-294 (2010).
Summary: 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.
For the entire collection see [Zbl 1196.68008].

MSC:

68W30 Symbolic computation and algebraic computation
14T05 Tropical geometry (MSC2010)
52B11 \(n\)-dimensional polytopes
52B55 Computational aspects related to convexity

Software:

cdd; gmp; TOPCOM; Gfan; SoPlex
PDFBibTeX XMLCite
Full Text: DOI