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.