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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
    • BergmanFan -- the Bergman fan of a matroid
    • isBalanced -- checks whether a tropical cycle is balanced
    • isTropicalBasis -- checks if a list of polynomials is a tropical basis for the ideal they generate
    • multiplicities -- returns the list of multiplicities on maximal cones in a tropical cycle
    • stableIntersection -- computes the stable intersection of two tropical varieties
    • tropicalCycle -- constructs a TropicalCycle from a Fan and a list with multiplicities
    • tropicalPrevariety -- the intersection of the tropical hypersurfaces
    • tropicalVariety -- the tropical variety associated to an ideal
    • visualizeHypersurface -- visualize the tropical hypersurface of the given polynomial
  • 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 (missing documentation)

For the programmer

The object Tropical is a package.