@book{tropicalbook,
  title={Introduction to Tropical Geometry: },
  author={Maclagan, D. and Sturmfels, B.},
  isbn={9780821851982},
  lccn={2014036141},
  series={Graduate Studies in Mathematics},
  url={https://books.google.com.tw/books?id=3DLMoQEACAAJ},
  year={2015},
  publisher={American Mathematical Society}
}
@article{allermannRau,
author = {Lars Allermann and Johannes Rau},
title = {First steps in tropical intersection theory},
journal = {Mathematische Zeitschrift},
publisher = {Springer},
  year      = {2009}
}


@inproceedings{AGK,
author = {Beatrice Amrhein and Oliver Gloor and Wolfgang K\"uchlin},
title = {Walking faster},
booktitle = {Proceedings DISCO '96},
publisher = {LNCS 1128, Springer},
address = {Berlin},
year = {1996},
pages = {150-161}
}

@article{AGK2,
author = {Beatrice Amrhein and Oliver Gloor and Wolfgang K\"uchlin},
title = {Walking faster.},
journal = {Proceedings DISCO '96},
publisher = {LNCS 1128, Springer},
address = {Berlin},
  year      = {1996},
  pages     = {150-161},
}

@book{atiyah,
    AUTHOR = {Atiyah, M. F. and Macdonald, I. G.},
     TITLE = {Introduction to commutative algebra},
 PUBLISHER = {Addison-Wesley Publishing Co., Reading, Mass.-London-Don
              Mills, Ont.},
      YEAR = {1969},
     PAGES = {ix+128},
   MRCLASS = {13.00},
  MRNUMBER = {MR0242802 (39 \#4129)},
MRREVIEWER = {J. A. Johnson},
}

@article {af-rse-96,
    AUTHOR = {Avis, David and Fukuda, Komei},
     TITLE = {Reverse search for enumeration},
      NOTE = {First International Colloquium on Graphs and Optimization
              (GOI), 1992 (Grimentz)},
   JOURNAL = {Discrete Appl. Math.},
  FJOURNAL = {Discrete Applied Mathematics. The Journal of Combinatorial
              Algorithms, Informatics and Computational Sciences},
    VOLUME = {65},
      YEAR = {1996},
    NUMBER = {1-3},
     PAGES = {21--46},
      ISSN = {0166-218X},
     CODEN = {DAMADU},
   MRCLASS = {05C30 (05A15)},
  MRNUMBER = {MR1380066 (98a:05080)},
}

@article{avis,
  author    = {David Avis and
               Komei Fukuda},
  title     = {A basis enumeration algorithm for convex hulls and vertex enumeration of arrangements and polyhedra.},
  journal   = {Discrete Computational Geometry},
  volume    = {8},
  year      = {1992},
  pages     = {295-313},
}


@book {basu,
    AUTHOR = {Basu, Saugata and Pollack, Richard and Roy,
              Marie-Fran{\c{c}}oise},
     TITLE = {Algorithms in real algebraic geometry},
    SERIES = {Algorithms and Computation in Mathematics},
    VOLUME = {10},
   EDITION = {Second},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {2006},
     PAGES = {x+662},
      ISBN = {978-3-540-33098-1; 3-540-33098-4},
   MRCLASS = {14P10 (03C10 52C45 68Q25 68W30)},
  MRNUMBER = {MR2248869 (2007b:14125)},
}

@article {bayer,
    AUTHOR = {Bayer, David and Morrison, Ian},
     TITLE = {Standard bases and geometric invariant theory. {I}. {I}nitial
              ideals and state polytopes},
      NOTE = {Computational aspects of commutative algebra},
   JOURNAL = {J. Symbolic Comput.},
  FJOURNAL = {Journal of Symbolic Computation},
    VOLUME = {6},
      YEAR = {1988},
    NUMBER = {2-3},
     PAGES = {209--217},
      ISSN = {0747-7171},
   MRCLASS = {13-04 (13B25 68Q40)},
  MRNUMBER = {MR988413 (90e:13001)},
MRREVIEWER = {Ferdinando Mora},
}

@book{becker,
    AUTHOR = {Becker, Thomas and Weispfenning, Volker},
     TITLE = {Gr\"obner bases},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {141},
      NOTE = {A computational approach to commutative algebra,
              In cooperation with Heinz Kredel},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1993},
     PAGES = {xxii+574},
      ISBN = {0-387-97971-9},
   MRCLASS = {13P10 (13-01)},
  MRNUMBER = {MR1213453 (95e:13018)},
MRREVIEWER = {J{\"o}rgen Backelin},
}

@article {Ber,
    AUTHOR = {Bergman, George M.},
     TITLE = {The logarithmic limit-set of an algebraic variety},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {157},
      YEAR = {1971},
     PAGES = {459--469},
      ISSN = {0002-9947},
   MRCLASS = {14.01},
  MRNUMBER = {MR0280489 (43 \#6209)},
MRREVIEWER = {M. J. Greenberg},
}

@preamble{
   "\def\cprime{$'$} "
}
@article {MR0435072,
    AUTHOR = {Bernstein, D. N.},
     TITLE = {The number of roots of a system of equations},
   JOURNAL = {Funkcional. Anal. i Prilo\v zen.},
  FJOURNAL = {Akademija Nauk SSSR. Funkcional\cprime nyi Analiz i ego
              Prilo\v zenija},
    VOLUME = {9},
      YEAR = {1975},
    NUMBER = {3},
     PAGES = {1--4},
      ISSN = {0374-1990},
   MRCLASS = {14B99 (12E99 58C25)},
  MRNUMBER = {MR0435072 (55 \#8034)},
MRREVIEWER = {A. H. Wallace},
}

@article{bernstein,
  author    = {David Bernstein},
  title     = {The number of roots of a system of equations},
  journal   = {Functional Analysis and its Applications},
  volume    = {9},
  number    = {},
  year      = {1975},
  pages     = {183-185},
}

@article{BG,
    AUTHOR = {Bieri, Robert and Groves, J. R. J.},
     TITLE = {The geometry of the set of characters induced by valuations},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
    VOLUME = {347},
      YEAR = {1984},
     PAGES = {168--195},
      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {14A20 (12J20 13A18 52A25)},
  MRNUMBER = {MR733052 (86c:14001)},
MRREVIEWER = {Ralph Strebel},
}

@article{BF,
author = {G\"oran Bj\"orck and Ralf Fr\"oberg}, 
title = {A faster way to count the solutions of inhomogeneous systems 
         of algebraic equations, with applications to cyclic $n$-roots}, 
journal = {J. Symb. Comput.},
volume = {12}, 
number = {3/4}, 
year =  {1991}, 
pages = {329-336}
}


@article {circuitideals,
    AUTHOR = {Bogart, Tristram and Jensen, Anders N. and Thomas, Rekha R.},
     TITLE = {The circuit ideal of a vector configuration},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {309},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {518--542},
      ISSN = {0021-8693},
     CODEN = {JALGA4},
   MRCLASS = {13Pxx (05Exx)},
  MRNUMBER = {MR2303191},
    eprint = {math.AC/0508628}
}

@article{ctvgammel,
  author    = {Tristram Bogart and
               Anders Jensen and
               Rekha Thomas and
               David Speyer and
               Bernd Sturmfels},
  title     = {Computing tropical varieties.},
  journal   = {J. Symb. Comput.},
  volume    = {42},
  number    = {1-2},
  year      = {2007},
  pages     = {54-73},
  bibsource = {},
  eprint = {math.AG/0507563}
}

@article {ctv,
    AUTHOR = {Bogart, T. and Jensen, A. N. and Speyer, D. and Sturmfels, B.
              and Thomas, R. R.},
     TITLE = {Computing tropical varieties},
   JOURNAL = {J. Symbolic Comput.},
  FJOURNAL = {Journal of Symbolic Computation},
    VOLUME = {42},
      YEAR = {2007},
    NUMBER = {1-2},
     PAGES = {54--73},
      ISSN = {0747-7171},
   MRCLASS = {14Qxx (68N30)},
  MRNUMBER = {MR2284285},
  eprint = {math.AG/0507563}
}

@misc{Buch,
  author    = {Bruno Buchberger},
  title     = {An Algorithm for Finding a Basis for the Residue Class
Ring of a Zero-Dimensional Polynomial Ideal},
  year      = {1965},
  note = {PhD-thesis (German)},
}

@article {collart,
    AUTHOR = {Collart, S. and Kalkbrener, M. and Mall, D.},
     TITLE = {Converting bases with the {G}r\"obner walk},
      NOTE = {Computational algebra and number theory (London, 1993)},
   JOURNAL = {J. Symbolic Comput.},
  FJOURNAL = {Journal of Symbolic Computation},
    VOLUME = {24},
      YEAR = {1997},
    NUMBER = {3-4},
     PAGES = {465--469},
      ISSN = {0747-7171},
   MRCLASS = {13P10 (68Q40)},
  MRNUMBER = {MR1484492},
}

@book {Cox97,
    AUTHOR = {Cox, David and Little, John and O'Shea, Donal},
     TITLE = {Ideals, varieties, and algorithms},
    SERIES = {Undergraduate Texts in Mathematics},
   EDITION = {Second},
      NOTE = {An introduction to computational algebraic geometry and
              commutative algebra},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1997},
     PAGES = {xiv+536},
      ISBN = {0-387-94680-2},
   MRCLASS = {13P10 (13-01 14-01 14Qxx 68Q40)},
  MRNUMBER = {MR1417938 (97h:13024)},
}


@article {develin-2004-9,
    AUTHOR = {Develin, Mike and Sturmfels, Bernd},
     TITLE = {Erratum for: ``{T}ropical convexity'' [{D}oc. {M}ath. {\bf 9}
              (2004), 1--27 (electronic); MR2054977]},
   JOURNAL = {Doc. Math.},
  FJOURNAL = {Documenta Mathematica},
    VOLUME = {9},
      YEAR = {2004},
     PAGES = {205--206 (electronic)},
      ISSN = {1431-0635},
   MRCLASS = {52A30 (92B10)},
  MRNUMBER = {MR2117413 (2006c:52005)},
MRREVIEWER = {Gerard Sierksma},
}

@misc {draisma,
 author = "Jan Draisma",
 title  = "A tropical approach to secant dimensions",
 year   = "2006",
 eprint  = "math.AG/0605345v3"
}

@PhdThesis{thesis,
  author    = {Anders Nedergaard Jensen},
  title        = {Algorithmic aspects of {G}r\"obner fans and tropical varieties},
  school       = {University of Aarhus},
  year         = {2007},
  note         = {\url{http://www.imf.au.dk/publs?id=655}},
}

@Misc{cats,
      author = {Jensen, Anders},
      title = {{CaTS}, a software system for toric state polytopes},
      howpublished = {Available at {http://www.soopadoopa.dk/anders/cats/cats.html}}
}


@article {lind,
    AUTHOR = {Einsiedler, Manfred and Kapranov, Mikhail and Lind, Douglas},
     TITLE = {Non-{A}rchimedean amoebas and tropical varieties},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
    VOLUME = {601},
      YEAR = {2006},
     PAGES = {139--157},
      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {14Gxx (14Pxx)},
  MRNUMBER = {MR2289207},
}


@article {FGLM,
    AUTHOR = {Faug{\`e}re, J. C. and Gianni, P. and Lazard, D. and Mora, T.},
     TITLE = {Efficient computation of zero-dimensional {G}r\"obner bases by
              change of ordering},
   JOURNAL = {J. Symbolic Comput.},
  FJOURNAL = {Journal of Symbolic Computation},
    VOLUME = {16},
      YEAR = {1993},
    NUMBER = {4},
     PAGES = {329--344},
      ISSN = {0747-7171},
   MRCLASS = {68Q40},
  MRNUMBER = {MR1263871 (94k:68095)},
}


@manual{cdd
, author =	"Komei Fukuda"
, title =	"cddlib reference manual, cddlib Version 094b"
, organization =	"~Swiss Federal Institute  of Technology"
, address =	"Lausanne and Z{\"u}rich, Switzerland"
, year =	2005
, sortkey =	"0051"
, note =	"\url{http://www.ifor.math.ethz.ch/~fukuda/cdd_home/cdd.html}"
, update =	"99.10 fukuda"
}

@article{fukuda,
  author    = {Komei Fukuda and Anders Jensen and Rekha Thomas},
  title     = {Computing {G}r{\"o}bner Fans.},
  journal   = {Mathematics of Computation, to appear},
  volume    = {},
  number    = {},
  year      = {2007},
  pages     = {},
  bibsource = {},
  eprint = {math.AC/0509544}
}


@article {genericgroebnerwalk,
    AUTHOR = {Fukuda, K. and Jensen, A. N. and Lauritzen, N. and Thomas, R.},
     TITLE = {The generic {G}r\"obner walk},
   JOURNAL = {J. Symbolic Comput.},
  FJOURNAL = {Journal of Symbolic Computation},
    VOLUME = {42},
      YEAR = {2007},
    NUMBER = {3},
     PAGES = {298--312},
      ISSN = {0747-7171},
   MRCLASS = {68W30},
  MRNUMBER = {MR2292637},
  eprint    = {math.AC/0501345}
}

@article{genericgroebnerwalkgammel,
  author    = {Komei Fukuda and Anders Jensen and Niels Lauritzen and Rekha Thomas},
  title     = {The generic {G}r\"obner walk.},
  journal   = {J. Symb. Comput.},
  volume    = {42},
  number    = {3},
  year      = {2007},
  pages     = {298-312},
  bibsource = {},
  eprint    = {math.AC/0501345}
}

@inproceedings{weibel,
  author    = {Christophe Weibel and
               Komei Fukuda},
  title     = {Computing faces up to k dimensions of a Minkowski Sum of
               Polytopes.},
  booktitle = {CCCG},
  year      = {2005},
  pages     = {256-259},
  ee        = {http://www.cccg.ca/proceedings/2005/44.pdf},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

@book {Ful,
    AUTHOR = {Fulton, William},
     TITLE = {Introduction to toric varieties},
    SERIES = {Annals of Mathematics Studies},
    VOLUME = {131},
      NOTE = {,
              The William H. Roever Lectures in Geometry},
 PUBLISHER = {Princeton University Press},
   ADDRESS = {Princeton, NJ},
      YEAR = {1993},
     PAGES = {xii+157},
      ISBN = {0-691-00049-2},
   MRCLASS = {14M25 (14-02 14J30)},
  MRNUMBER = {MR1234037 (94g:14028)},
MRREVIEWER = {T. Oda},
}
@article {li,
    AUTHOR = {Gao, Tangan and Li, T. Y.},
     TITLE = {Mixed volume computation via linear programming},
   JOURNAL = {Taiwanese J. Math.},
  FJOURNAL = {Taiwanese Journal of Mathematics},
    VOLUME = {4},
      YEAR = {2000},
    NUMBER = {4},
     PAGES = {599--619},
      ISSN = {1027-5487},
   MRCLASS = {65D18 (52A39)},
  MRNUMBER = {MR1799755 (2001j:65026)},
}




@article{gathmann,
  author = {Andreas Gathmann},
  title = {Tropical Algebraic Geometry},
  eprint    = {math.AG/0601322},
  year = {2006}
}


@incollection{polymake,
  author =       {Ewgenij Gawrilow and Michael Joswig},
  title =        {polymake: a Framework for Analyzing Convex Polytopes},
  pages =        {43-74},
  editor =       {Gil Kalai and G\"unter M. Ziegler},
  booktitle =    {Polytopes --- Combinatorics and Computation},
  publisher =    {Birkh\"auser},
  year =         {2000}
}

@article {gianni88,
    AUTHOR = {Gianni, Patrizia and Trager, Barry and Zacharias, Gail},
     TITLE = {Gr\"obner bases and primary decomposition of polynomial
              ideals},
      NOTE = {Computational aspects of commutative algebra},
   JOURNAL = {J. Symbolic Comput.},
  FJOURNAL = {Journal of Symbolic Computation},
    VOLUME = {6},
      YEAR = {1988},
    NUMBER = {2-3},
     PAGES = {149--167},
      ISSN = {0747-7171},
   MRCLASS = {68Q40 (13-04 13A17)},
  MRNUMBER = {MR988410 (90f:68091)},
MRREVIEWER = {Daniel Lazard},
}


@Misc{gfan,
     author = {Jensen, Anders Nedergaard},
     title = {Gfan, a software system for {G}r{\"o}bner fans},
     howpublished = {Available at \url{http://home.imf.au.dk/ajensen/software/gfan/gfan.html}}
} 

@misc{gmp,
        author = {Torbj{\"o}rn {Granlund et al.}},
        title = "{GNU} Multiple Precision Arithmetic Library 4.1.2",
        month = {December},
        year = 2002,
        note = "\url{http://swox.com/gmp/}"
}

@book {greuelpfister,
    AUTHOR = {Greuel, Gert-Martin and Pfister, Gerhard},
     TITLE = {A {S}ingular introduction to commutative algebra},
      NOTE = {With contributions by Olaf Bachmann, Christoph Lossen and Hans
              Sch\"onemann,
              With 1 CD-ROM (Windows, Macintosh, and UNIX)},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {2002},
     PAGES = {xviii+588},
      ISBN = {3-540-42897-6},
   MRCLASS = {13-01 (13-04)},
  MRNUMBER = {MR1930604 (2003k:13001)},
MRREVIEWER = {Paulo F. Machado},
}


@article {hampton,
    AUTHOR = {Hampton, Marshall and Moeckel, Richard},
     TITLE = {Finiteness of relative equilibria of the four-body problem},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {163},
      YEAR = {2006},
    NUMBER = {2},
     PAGES = {289--312},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {70F10},
  MRNUMBER = {MR2207019},
}

@article {hubersturmfels,
    AUTHOR = {Huber, Birkett and Sturmfels, Bernd},
     TITLE = {A polyhedral method for solving sparse polynomial systems},
   JOURNAL = {Math. Comp.},
  FJOURNAL = {Mathematics of Computation},
    VOLUME = {64},
      YEAR = {1995},
    NUMBER = {212},
     PAGES = {1541--1555},
      ISSN = {0025-5718},
}

@misc{TrIm,
    AUTHOR = { Bernd Sturmfels and Josephine Yu} ,
 title = "Tropical Implicitization and Mixed Fiber Polytopes",
        year = 2007,
  eprint    = {cs.SC/0706.0564v1}
}

@misc{jensenMaster,
    AUTHOR = { Anders Nedergaard Jensen},
 title = {Computing {G}r\"obner fans of toric ideals},
        year = 2002,
  note    = {Master thesis, University of Aarhus}
}



@InProceedings{jensenICMS2006,
  author    = {Anders Nedergaard Jensen},
  title     = {A presentation of the {Gfan} software.},
  booktitle    = "Mathematical Software - ICMS 2006",
  pages        = "222--224",
  year         = 2006,
  editor       = "Iglesias and Takayama",
  publisher    = "Springer",
  ISBN         = "3540380841",
}

@article {jensen,
    AUTHOR = {Jensen, Anders Nedergaard},
     TITLE = {A non-regular {G}r\"obner fan},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {37},
      YEAR = {2007},
    NUMBER = {3},
     PAGES = {443--453},
      ISSN = {0179-5376},
     CODEN = {DCGEER},
   MRCLASS = {13P10},
  MRNUMBER = {MR2301528},
  eprint    = {math.CO/0501352}
}

@misc{symmetricfans,
  author  = {Jensen, Anders N.},
  title   = {Traversing symmetric polyhedral fans},
  howpublished = {to appear in ``Mathe\-matical Software - ICMS 2010''},
  booktitle    = "Mathematical Software - ICMS 2010",
  year         = 2010,
  publisher    = "Springer",
}

@article {kalkbrener-onthecomplexity,
    AUTHOR = {Kalkbrener, Michael},
     TITLE = {On the complexity of {G}r\"obner bases conversion},
      NOTE = {Polynomial elimination---algorithms and applications},
   JOURNAL = {J. Symbolic Comput.},
  FJOURNAL = {Journal of Symbolic Computation},
    VOLUME = {28},
      YEAR = {1999},
    NUMBER = {1-2},
     PAGES = {265--273},
      ISSN = {0747-7171},
   MRCLASS = {13P10 (68W30)},
  MRNUMBER = {MR1709906 (2000g:13020)},
MRREVIEWER = {Joachim Apel},
}



@misc {katz,
 author = "Eric Katz",
 title  = "A tropical toolkit",
 year   = "2006",
 eprint  = "math.AG/0610878v2"
}


@misc {mlfb,
 author = "Anders Nedergaard Jensen and
           Niels Lauritzen and
           Bjarke Hammersholt Roune",
 title  = "Maximal lattice free bodies, test sets and the Frobenius problem",
 year   = "2007",
 eprint  = "arXiv:0705.4483"
}

@book {lauritzen-concrete,
    AUTHOR = {Lauritzen, Niels},
     TITLE = {Concrete abstract algebra},
      NOTE = {From numbers to Gr\"obner bases},
 PUBLISHER = {Cambridge University Press},
   ADDRESS = {Cambridge},
      YEAR = {2003},
     PAGES = {xiv+240},
      ISBN = {0-521-53410-0},
   MRCLASS = {00-01 (13-01 20-01)},
  MRNUMBER = {MR2014325 (2005d:00001)},
MRREVIEWER = {Frank Sottile},
}

@article{lauritzen,
  author    = {Niels Lauritzen},
  title     = {Truncated {G}r\"obner fans and lattice ideals},
  journal   = {},
  volume    = {},
  year      = {2005},
  eprint    = {math.AG/0509247}
}

@incollection {mall,
    AUTHOR = {Mall, Daniel},
     TITLE = {Gr\"obner fans and projective schemes},
 BOOKTITLE = {Symbolic rewriting techniques (Ascona, 1995)},
    SERIES = {Progr. Comput. Sci. Appl. Logic},
    VOLUME = {15},
     PAGES = {181--191},
 PUBLISHER = {Birkh\"auser},
   ADDRESS = {Basel},
      YEAR = {1998},
   MRCLASS = {13P10 (68Q40)},
  MRNUMBER = {MR1624580 (99d:13033)},
MRREVIEWER = {Ralf Fr{\"o}berg},
}



@misc{mikhalkin,
   author    = {Grigory Mikhalkin},
   title     = {Tropical geometry},
   year      = {2007},
   note   = {Work in progress, http://www.math.toronto.edu/mikha/TG-project.html},
}


@incollection {doubledescription,
    AUTHOR = {Motzkin, T. S. and Raiffa, H. and Thompson, G. L. and Thrall,
              R. M.},
     TITLE = {The double description method},
 BOOKTITLE = {Contributions to the theory of games, vol. 2},
    SERIES = {Annals of Mathematics Studies, no. 28},
     PAGES = {51--73},
 PUBLISHER = {Princeton University Press},
   ADDRESS = {Princeton, N. J.},
      YEAR = {1953},
   MRCLASS = {90.0X},
  MRNUMBER = {MR0060202 (15,638g)},
MRREVIEWER = {H. W. Kuhn},
}

@book{ascb,
   author    = {Lior Pachter and Bernd Sturmfelse},
   title     = {Algebraic Statistics for Computational Biology},
   year      = {2005},
 PUBLISHER = {Cambridge Univ. Press},
   ADDRESS = {New York},
}

@article{rambau,
  author    = {J{\"o}rg Rambau},
  title     = {{TOPCOM}: Triangulations of Point Configurations and Oriented Matroids},
  journal   = {ZIB report},
  institution ={Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin},
  volume    = {02-17},
  year      = {2002},
}

@TechReport{singular,
  author = 	 {G.-M. Greuel and G. Pfister and H. Sch\"onemann},
  title = 	 {{\sc Singular} 2.0.5},
  type =         {{A Computer Algebra System for Polynomial Computations}},
  institution =  {Centre for Computer Algebra},
  address = 	 {University of Kaiserslautern},
  year =         {2004},
  note = 	 {\url{http://www.singular.uni-kl.de}},
}

@Misc{4ti2,
  author =   {4ti2 team},
  title =    {4ti2---A software package for algebraic, geometric and 
              combinatorial problems on linear spaces},
  howpublished = {{A}vailable at www.4ti2.de}
}

@article{huber,
  author    = {Birkett Huber and
               Rekha R. Thomas},
  title     = {Computing {G}r{\"o}bner fans of toric ideals.},
  journal   = {Experimental Mathematics},
  volume    = {9},
  number    = {3/4},
  year      = {2000},
  pages     = {321-331}
}

@misc{singularscript,
        author = {Anders Nedergaard Jensen},
        title = "A {S}ingular script for verifying a {Gr{\"o}bner} fan computation.",
        year = 2005,
        note = "\url{http://home.imf.au.dk/ajensen/papers/singularscript.html}"
}

@article{lifting,
  author    = {Hannah Markwig and Thomas Markwig and Anders Jensen},
  title     = {An Algorithm for Lifting Points in a Tropical Variety},
  journal   = {},
  volume    = {},
  pages     = {},
  year      = {2007},
  eprint = {math.AG/0705.2441}
}

@article{Kalk,
  author    = {Michael Kalkbrener},
  title     = {On the complexity of {G}r{\"o}bner bases conversion},
  journal   = {J. Symb. Comput.},
  volume    = {28},
  year      = {1999},
  pages     = {265--273}
}


@article {MoRo,
    AUTHOR = {Mora, Teo and Robbiano, Lorenzo},
     TITLE = {The {G}r\"obner fan of an ideal},
      NOTE = {Computational aspects of commutative algebra},
   JOURNAL = {J. Symbolic Comput.},
  FJOURNAL = {Journal of Symbolic Computation},
    VOLUME = {6},
      YEAR = {1988},
    NUMBER = {2-3},
     PAGES = {183--208},
      ISSN = {0747-7171},
   MRCLASS = {13A15 (13-04 68Q40)},
  MRNUMBER = {MR988412 (90d:13004)},
MRREVIEWER = {Felipe Cucker},
}

@article{onn,
  author    = {Shmuel Onn and
               Bernd Sturmfels},
  title     = {Cutting corners},
  journal   = {Advances in Applied Mathematics},
  volume    = {23},
  number    = {},
  year      = {1999},
  pages     = {29-48}
}

@incollection {richtergebert-2003-,
    AUTHOR = {Richter-Gebert, J{\"u}rgen and Sturmfels, Bernd and Theobald,
              Thorsten},
     TITLE = {First steps in tropical geometry},
 BOOKTITLE = {Idempotent mathematics and mathematical physics},
    SERIES = {Contemp. Math.},
    VOLUME = {377},
     PAGES = {289--317},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2005},
   MRCLASS = {14P99 (52B70 68W30)},
  MRNUMBER = {MR2149011 (2006d:14073)},
MRREVIEWER = {Eugenii Shustin},
eprint = {math.AG/0306366},
}

@incollection {robbiano,
    AUTHOR = {Robbiano, Lorenzo},
     TITLE = {Term orderings on the polynomial ring},
 BOOKTITLE = {EUROCAL '85, Vol.\ 2 (Linz, 1985)},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {204},
     PAGES = {513--517},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1985},
   MRCLASS = {13B25 (06F15 32B05)},
  MRNUMBER = {MR826583 (87e:13006)},
MRREVIEWER = {David C. Lantz},
}

@book {saito,
    AUTHOR = {Saito, Mutsumi and Sturmfels, Bernd and Takayama, Nobuki},
     TITLE = {Gr\"obner deformations of hypergeometric differential
              equations},
    SERIES = {Algorithms and Computation in Mathematics},
    VOLUME = {6},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {2000},
     PAGES = {viii+254},
      ISBN = {3-540-66065-8},
   MRCLASS = {13N10 (13P10 16S32 32C38 33C80 68W30)},
  MRNUMBER = {MR1734566 (2001i:13036)},
MRREVIEWER = {Francisco Jes{\'u}s Castro-Jim{\'e}nez},
}


@article {tropgrass,
    AUTHOR = {Speyer, David and Sturmfels, Bernd},
     TITLE = {The tropical {G}rassmannian},
   JOURNAL = {Adv. Geom.},
  FJOURNAL = {Advances in Geometry},
    VOLUME = {4},
      YEAR = {2004},
    NUMBER = {3},
     PAGES = {389--411},
      ISSN = {1615-715X},
     CODEN = {AGDEA3},
   MRCLASS = {14P99 (13J30 14M25)},
  MRNUMBER = {MR2071813 (2005d:14089)},
MRREVIEWER = {Meirav Amram-Blei},
eprint = {math.AG/0304218},
}

@book {stoustrup,
    AUTHOR = {Stoustrup, Bjarne},
     TITLE = {The C++ Programming Language},
 PUBLISHER = {Addison-Wesley},
   EDITION = {Third},
      YEAR = {1997},
      ISBN = {0-201-88954-4},
}


@book {sturmfels,
    AUTHOR = {Sturmfels, Bernd},
     TITLE = {Gr\"obner bases and convex polytopes},
    SERIES = {University Lecture Series},
    VOLUME = {8},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {1996},
     PAGES = {xii+162},
      ISBN = {0-8218-0487-1},
   MRCLASS = {13P10 (14M25 52B20)},
  MRNUMBER = {MR1363949 (97b:13034)},
MRREVIEWER = {P. Schenzel},
}


@book {sturmfelssolving,
    AUTHOR = {Sturmfels, Bernd},
     TITLE = {Solving systems of polynomial equations},
    SERIES = {CBMS Regional Conference Series in Mathematics},
    VOLUME = {97},
 PUBLISHER = {Published for the Conference Board of the Mathematical
              Sciences, Washington, DC},
      YEAR = {2002},
     PAGES = {viii+152},
      ISBN = {0-8218-3251-4},
   MRCLASS = {13P10 (14P99 14Q15 62-09 65H10)},
  MRNUMBER = {MR1925796 (2003i:13037)},
MRREVIEWER = {Joseph Gubeladze},
}

@article{sturmfelstevelev,
  author = {Bernd Sturmfels and Jenia Tevelev},
  title = {Elimination Theory for Tropical Varieties},
  eprint = {math.AG/0704.3471v1},
  year = {2007}
}

@article {theobald,
    AUTHOR = {Theobald, Thorsten},
     TITLE = {On the frontiers of polynomial computations in tropical
              geometry},
   JOURNAL = {J. Symbolic Comput.},
  FJOURNAL = {Journal of Symbolic Computation},
    VOLUME = {41},
      YEAR = {2006},
    NUMBER = {12},
     PAGES = {1360--1375},
      ISSN = {0747-7171},
   MRCLASS = {68Q17 (14P25 14Q15 68Q15 68Q25)},
  MRNUMBER = {MR2271330 (2007g:68052)},
MRREVIEWER = {Luis Felipe Tabera},
eprint = {math.CO/0411012},
}

@article {tran,
    AUTHOR = {Tran, Quoc-Nam},
     TITLE = {A fast algorithm for {G}r\"obner basis conversion and its
              applications},
   JOURNAL = {J. Symbolic Comput.},
  FJOURNAL = {Journal of Symbolic Computation},
    VOLUME = {30},
      YEAR = {2000},
    NUMBER = {4},
     PAGES = {451--467},
      ISSN = {0747-7171},
   MRCLASS = {13P10 (68W30)},
  MRNUMBER = {MR1784752 (2001k:13043)},
MRREVIEWER = {Petr Lison{\v{e}}k},
}

@article{Traverso,
  author    = {Carlo Traverso},
  title     = {Hilbert functions and {B}uchberger algorithm},
  journal   = {J. Symb. Comput.},
  volume    = {22},
  year      = {1996},
  pages     = {355--376}
}

@article{vigeland-2004-,
  author = {Magnus Dehli Vigeland},
  title = {The group law on a tropical elliptic curve},
  url = {http://www.citebase.org/cgi-bin/citations?id=oai:arXiv.org:math/0411485},
  eprint    = {math.AG/0411485},
  year = {2004}
}

@PhdThesis{wunderling,
  author       = "Roland Wunderling",
  title        = "Paralleler und objektorientierter {S}implex-{A}lgorithmus",
  school       = "Technische Universit{\"a}t Berlin",
  year         = "1996",
  note         = "\url{http://www.zib.de/Publications/abstracts/TR-96-09/}",
}

@book{ziegler,
   author    = {G{\"u}nter Ziegler},
   title     = {Lectures on Polytopes},
   year      = {1994},
   publisher = {Springer-Verlag},
   volume    = {152},
   series    = {GTM},
}




