References
Baccelli, F.L., Cohen, G., Olsder, G.J., Quadrat, J.-P.: Synchronization and Linearity: An Algebra for Discrete Event Systems. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. Wiley, Chichester (1992)
Bieri, R., Groves, J.R.J.: The geometry of the set of characters induced by valuations. J. Reine Angew. Math. 347, 168–195 (1984)
Bogart, T., Jensen, A.N., Speyer, D., Sturmfels, B., Thomas, R.R.: Computing tropical varieties. J. Symb. Comput. 42(1–2), 54–73 (2007)
Cox, D.A., Little, J., O’Shea, D.: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 4th edn. Undergraduate Texts in Mathematics. Springer, Cham (2015)
Cox, D.A., Little, J.B., Schenck, H.K.: Toric Varieties. Graduate Studies in Mathematics, vol. 124. American Mathematical Society, Providence (2011)
Einsiedler, M., Kapranov, M., Lind, D.: Non-Archimedean amoebas and tropical varieties. J. Reine Angew. Math. 601, 139–157 (2006)
Gawrilow, E., Joswig, M.: Polymake: a framework for analyzing convex polytopes, polytopes—combinatorics and computation. In: DMV Sem., vol. 29, Oberwolfach 1997, pp. 43–73. Birkhäuser, Basel (2000). Software available at http://polymake.org
Jensen, A.N.: Gfan, a software system for Gröbner fans and tropical varieties, version 0.5. (2011). Available at http://home.imf.au.dk/jensen/software/gfan/gfan.html
Kontsevich, M.: Intersection theory on the moduli space of curves and the matrix Airy function. Commun. Math. Phys. 147(1), 1–23 (1992)
Mikhalkin, G.: Enumerative tropical algebraic geometry in \(\mathbb{R}^{2}\). J. Am. Math. Soc. 18(2), 313–377 (2005)
Richter-Gebert, J., Sturmfels, B., Theobald, T.: First Steps in Tropical Geometry, Idempotent Mathematics and Mathematical Physics. Contemp. Math., vol. 377, pp. 289–317. Amer. Math. Soc., Providence (2005)
Speyer, D., Sturmfels, B.: The tropical Grassmannian. Adv. Geom. 4(3), 389–411 (2004)
Sturmfels, B.: Gröbner Bases and Convex Polytopes. University Lecture Series, vol. 8. American Mathematical Society, Providence (1996)
Ziegler, G.M.: Lectures on Polytopes. Graduate Texts in Mathematics, vol. 152. Springer, New York (1995)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Joswig, M. Diane Maclagan, Bernd Sturmfels: “Introduction to Tropical Geometry”. Jahresber. Dtsch. Math. Ver. 118, 233–237 (2016). https://doi.org/10.1365/s13291-016-0133-6
Published:
Issue Date:
DOI: https://doi.org/10.1365/s13291-016-0133-6