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Tropical -- the main M2 package for tropical computations

Description

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.

Contributors

The following people have also contributed to the package:

Authors

Version

This documentation describes version 1.0 of Tropical.

Citation

If you have used this package in your research, please cite it as follows:

@misc{TropicalSource,
  title = {{Tropical: computations in tropical geometry. Version~1.0}},
  author = {Carlos Amendola and Kathlen Kohn and Sara Lamboglia and Diane Maclagan and Ben Smith and Jeff Sommars and Paolo Tripoli and Magdalena Zajaczkowska},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

Exports

  • 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 -- see visualizeHypersurface -- visualize the tropical hypersurface of the given polynomial

For the programmer

The object Tropical is a package, defined in Tropical.m2, with auxiliary files in Tropical/.


The source of this document is in Tropical.m2:837:0.