Computing tropical linear spaces. We define and study the cyclic Bergman fan of a matroid M, which is a simplicial polyhedral fan supported on the tropical linear space 𝒯(M) of M and is amenable to computational purposes. It slightly refines the nested set structure on 𝒯(M), and its rays are in bijection with flats of M which are either cyclic flats or singletons. We give a fast algorithm for calculating it, making some computational applications of tropical geometry now viable. Our C++ implementation, called TropLi, and a tool for computing vertices of Newton polytopes of A-discriminants, are both available online.
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References in zbMATH (referenced in 12 articles )
Showing results 1 to 12 of 12.
- Bocci, Cristiano; Carlini, Enrico; Kileel, Joe: Hadamard products of linear spaces (2016)
- Ren, Qingchun; Shaw, Kristin; Sturmfels, Bernd: Tropicalization of del Pezzo surfaces (2016)
- Linde, J.; de la Puente, M.J.: Matrices commuting with a given normal tropical matrix (2015)
- Hampe, Simon: a-tint: a polymake extension for algorithmic tropical intersection theory (2014)
- Ren, Qingchun; Sam, Steven V.; Sturmfels, Bernd: Tropicalization of classical moduli spaces (2014)
- Cattani, Eduardo; Cueto, María Angélica; Dickenstein, Alicia; Di Rocco, Sandra; Sturmfels, Bernd: Mixed discriminants (2013)
- Corel, Eduardo: Gérard-Levelt membranes (2013)
- Emiris, Ioannis Z.; Fisikopoulos, Vissarion; Konaxis, Christos; Peñaranda, Luis: An oracle-based, output-sensitive algorithm for projections of resultant polytopes (2013)
- Jensen, Anders; Yu, Josephine: Computing tropical resultants (2013)
- Rincón, Felipe: Computing tropical linear spaces (2013)
- Rincón, Felipe: Local tropical linear spaces (2013)
- Ardila, Federico; Klivans, Caroline J.: The Bergman complex of a matroid and phylogenetic trees (2006)