\def\cprime{$'$}
\begin{thebibliography}{10}

\bibitem{4ti2}
4ti2 team.
\newblock 4ti2---a software package for algebraic, geometric and combinatorial
  problems on linear spaces.
\newblock {A}vailable at www.4ti2.de.

\bibitem{allermannRau}
Lars Allermann and Johannes Rau.
\newblock First steps in tropical intersection theory.
\newblock {\em Mathematische Zeitschrift}, 2009.

\bibitem{avis}
David Avis and Komei Fukuda.
\newblock A basis enumeration algorithm for convex hulls and vertex enumeration
  of arrangements and polyhedra.
\newblock {\em Discrete Computational Geometry}, 8:295--313, 1992.

\bibitem{bg}
Robert Bieri and J.~R.~J. Groves.
\newblock The geometry of the set of characters induced by valuations.
\newblock {\em J. Reine Angew. Math.}, 347:168--195, 1984.

\bibitem{ctv}
T.~Bogart, A.~N. Jensen, D.~Speyer, B.~Sturmfels, and R.~R. Thomas.
\newblock Computing tropical varieties.
\newblock {\em J. Symbolic Comput.}, 42(1-2):54--73, 2007, math.AG/0507563.

\bibitem{Buch}
Bruno Buchberger.
\newblock An algorithm for finding a basis for the residue class ring of a
  zero-dimensional polynomial ideal, 1965.
\newblock PhD-thesis (German).

\bibitem{collart}
S.~Collart, M.~Kalkbrener, and D.~Mall.
\newblock Converting bases with the {G}r\"obner walk.
\newblock {\em J. Symbolic Comput.}, 24(3-4):465--469, 1997.
\newblock Computational algebra and number theory (London, 1993).

\bibitem{cdd}
Komei Fukuda.
\newblock {\em cddlib reference manual, cddlib Version 094b}.
\newblock ~Swiss Federal Institute of Technology, Lausanne and Z{\"u}rich,
  Switzerland, 2005.
\newblock \url{http://www.ifor.math.ethz.ch/~fukuda/cdd_home/cdd.html}.

\bibitem{fukuda}
Komei Fukuda, Anders Jensen, and Rekha Thomas.
\newblock Computing {G}r{\"o}bner fans.
\newblock {\em Mathematics of Computation, to appear}, 2007, math.AC/0509544.

\bibitem{polymake}
Ewgenij Gawrilow and Michael Joswig.
\newblock polymake: a framework for analyzing convex polytopes.
\newblock In Gil Kalai and G\"unter~M. Ziegler, editors, {\em Polytopes ---
  Combinatorics and Computation}, pages 43--74. Birkh\"auser, 2000.

\bibitem{gmp}
Torbj{\"o}rn {Granlund et al.}
\newblock {GNU} multiple precision arithmetic library 4.1.2, December 2002.
\newblock \url{http://swox.com/gmp/}.

\bibitem{huber}
Birkett Huber and Rekha~R. Thomas.
\newblock Computing {G}r{\"o}bner fans of toric ideals.
\newblock {\em Experimental Mathematics}, 9(3/4):321--331, 2000.

\bibitem{cats}
Anders Jensen.
\newblock {CaTS}, a software system for toric state polytopes.
\newblock Available at {http://www.soopadoopa.dk/anders/cats/cats.html}.

\bibitem{symmetricfans}
Anders~N. Jensen.
\newblock Traversing symmetric polyhedral fans.
\newblock to appear in ``Mathe\-matical Software - ICMS 2010'', 2010.

\bibitem{thesis}
Anders~Nedergaard Jensen.
\newblock {\em Algorithmic aspects of {G}r\"obner fans and tropical varieties}.
\newblock PhD thesis, University of Aarhus, 2007.
\newblock \url{http://www.imf.au.dk/publs?id=655}.

\bibitem{jensen}
Anders~Nedergaard Jensen.
\newblock A non-regular {G}r\"obner fan.
\newblock {\em Discrete Comput. Geom.}, 37(3):443--453, 2007, math.CO/0501352.

\bibitem{tropicalbook}
D.~Maclagan and B.~Sturmfels.
\newblock {\em Introduction to Tropical Geometry:}.
\newblock Graduate Studies in Mathematics. American Mathematical Society, 2015.

\bibitem{lifting}
Hannah Markwig, Thomas Markwig, and Anders Jensen.
\newblock An algorithm for lifting points in a tropical variety.
\newblock 2007, math.AG/0705.2441.

\bibitem{MoRo}
Teo Mora and Lorenzo Robbiano.
\newblock The {G}r\"obner fan of an ideal.
\newblock {\em J. Symbolic Comput.}, 6(2-3):183--208, 1988.
\newblock Computational aspects of commutative algebra.

\bibitem{rambau}
J{\"o}rg Rambau.
\newblock {TOPCOM}: Triangulations of point configurations and oriented
  matroids.
\newblock {\em ZIB report}, 02-17, 2002.

\bibitem{tropgrass}
David Speyer and Bernd Sturmfels.
\newblock The tropical {G}rassmannian.
\newblock {\em Adv. Geom.}, 4(3):389--411, 2004, math.AG/0304218.

\bibitem{sturmfels}
Bernd Sturmfels.
\newblock {\em Gr\"obner bases and convex polytopes}, volume~8 of {\em
  University Lecture Series}.
\newblock American Mathematical Society, Providence, RI, 1996.

\bibitem{sturmfelssolving}
Bernd Sturmfels.
\newblock {\em Solving systems of polynomial equations}, volume~97 of {\em CBMS
  Regional Conference Series in Mathematics}.
\newblock Published for the Conference Board of the Mathematical Sciences,
  Washington, DC, 2002.

\bibitem{wunderling}
Roland Wunderling.
\newblock {\em Paralleler und objektorientierter {S}implex-{A}lgorithmus}.
\newblock PhD thesis, Technische Universit{\"a}t Berlin, 1996.
\newblock \url{http://www.zib.de/Publications/abstracts/TR-96-09/}.

\end{thebibliography}
