Code
Software
(see below for description of selected items)
Y. Ren: the tropical package in OSCAR. available as part of the official OSCAR distribution (2023, latest version).
D. Bendle, T. Hofmann, Y. Ren: tropicalNewton.lib, a Singular library for tropical computations using Newton polygon methods. available as part of the official Singular distribution (2016, latest version).
A. N. Jensen, H. Markwig, T. Markwig, Y. Ren: tropical.lib, a Singular interface to polymake. available as part of the official Singular distribution (2016, latest version).
J. Boehm, S. Keicher, Y. Ren: gitfan.lib, a Singular library for computing GIT-fans. available as part of the official Singular distribution (2016, latest version).
T. Markwig, Y. Ren: polymake.lib, a Singular interface to polymake. available as part of the official Singular distribution (2016, latest version).
A. Jensen, Y. Ren, F. Seelisch: gfan.lib, a Singular interface to gfanlib and more. available as part of the official Singular distribution (2016, latest version).
F. Hinkelmann, L. Kastner, M. Stillmann, Y. Ren: Singular online, an online platform for Singular. available on the official Singular website (2016, latest version).
M. Marais, Y. Ren: graal.lib, a Singular library for localizations at prime ideals. available as part of the official Singular distribution (2015, latest version).
J. Boehm, L. Kastner, B. Lorenz, Y. Ren, H. Schönemann: divisors.lib, a Singular library for polyhedral divisors. available as part of the official Singular distribution (2012, latest version).
singular online
A webinterface for Singular, based on the InteractiveShell framework by Lars Kastner, Mike Stillman and Franziska Hinkelmann. Give it a try and don't forget to download input / output to save your work. Your data will be permanently lost otherwise!
tropicalNewton.lib
A Singular library for computing tropical varieties using Newton polygon methods. Albeit limited to trivial valuations (or the constant coefficient case), it is currently the fastest implementation for computing tropical varieties and supports symmetry. The algorithms are described in:
T. Hofmann, Y. Ren: Computing tropical points and tropical links (arXiv:1611.02878).
tropical.lib
A Singular library for various computations in tropical geometry, such as lifting points on tropical varieties, computing tropical J-invariants, computing intial forms and ideal and much more. Also features algorithms for computing tropical varieties: for the trivial valuations (or the constant coefficient case) it uses the classical algorithm developed in
T. Bogart, A. N. Jensen, D. Speyer, B. Sturmfels, R. R. Thomas: Computing tropical varieties, J. Symb. Comp. 42(1-2), 54–73. (2007).
for p-adic valuations it uses the algorithm developed in
T. Markwig, Y. Ren: Computing tropical varieties over fields with valuation, arXiv:1612.01762, 2016.
Also contains special visualization functions for tropicalizations of plane curves (both min and max).
