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Tropical :: Tropical

Tropical -- the main M2 package for tropical computations


This is the main M2 package for all tropical computations. This uses Anders Jensen's package gfan, Michael Joswig's package Polymake, and also internal M2 computations.

The package defaults to using the min convention for tropical geometry. To switch to the max convention, reload the package using the command loadPackage("Tropical",Configuration=>{"tropicalMax"=>true});

The main command is tropicalVariety.

To use the Polymake commands see the Polymake interface instructions.


The following people have also contributed to the package:



This documentation describes version 1.0 of Tropical.

Source code

The source code from which this documentation is derived is in the file Tropical.m2. The auxiliary files accompanying it are in the directory Tropical/.


  • Types
  • Functions and commands
  • Methods
  • Symbols
    • ComputeMultiplicities -- option to compute the multiplicities in case they ideal is not prime
    • IsHomogeneous -- option to declare if the input ideal is homogeneous
    • Prime -- option to declare if the input ideal is prime
    • Symmetry -- option to declare if the input ideal has symmetries
    • Valuation -- option to declare a valuation for tropicalization

For the programmer

The object Tropical is a package.