(see below for description of selected items)



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!



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).



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).