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:

- Types
- TropicalCycle -- a Type for working with tropical cycles

- Functions and commands
- 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
- tropicalVarietyWithVal -- EXPERIMENTAL: tropical variety with valuations
- visualizeHypersurface -- visualize the tropical hypersurface of the given polynomial

- Methods
- ambDim(TropicalCycle) -- computes the dimension of the ambient space of a tropical cycle
- cones(ZZ,TropicalCycle) -- computes the cones of a tropical cycle
- dim(TropicalCycle) -- computes the dimension of a tropical cycle
- fan(TropicalCycle) -- outputs the fan assocated to the tropical cycle
- fVector(TropicalCycle) -- computes the fVector of a tropical cycle
- isBalanced(TropicalCycle), see isBalanced -- checks whether a tropical cycle is balanced
- isPure(TropicalCycle) -- checks whether a tropical cycle is pure
- isSimplicial(TropicalCycle) -- checks whether a tropical cycle is simplicial
- linealitySpace(TropicalCycle) -- computes the lineality space of a tropical cycle
- maxCones(TropicalCycle) -- computes the maximal cone of a tropical cycle
- multiplicities(TropicalCycle), see multiplicities -- returns the list of multiplicities on maximal cones in a tropical cycle
- rays(TropicalCycle) -- computes the rays of a tropical cycle
- stableIntersection(TropicalCycle,TropicalCycle), see stableIntersection -- computes the stable intersection of two tropical varieties

- 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