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StatePolytope -- computes state polytopes of ideals

Description

StatePolytope computes state polytopes of ideals using the programs gfan, M2, and polymake. Specifically, it computes Statem(I) or State(I) as defined in Sturmfels's book Groebner bases and convex polytopes, page 14. There is also a function for testing GIT stability of an ideal in a polynomial ring with respect to action of the maximal torus scaling the variables.

We assume that the user has gfan version 0.3 or higher on his or her system. The default assumption is that the command to run gfan is gfan, but this can be changed in the package configuration if necessary. The user also needs polymake version 2.3-1 or higher installed on his or her system, and it must be run by this command. Finally, the user is responsible for making sure the ideal of study is supported by gfan. In version 0.3 this means the ideal must be in a polynomial ring over QQ or ZZ/p with p < 32749, and no variable's name should be a substring of another's.

Author

Version

This documentation describes version 1.2 of StatePolytope.

Citation

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

@misc{StatePolytopeSource,
  title = {{StatePolytope: the state polytope of an ideal. Version~1.2}},
  author = {Dave Swinarski},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

Exports

For the programmer

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


The source of this document is in StatePolytope.m2:117:0.