# ToricInvariants -- Given a projective toric variety, the package computes the degree and codimension of the dual, the Euclidean distance degree, polar degrees, and Chern-Mather class

## Description

Given a projective toric variety X_A defined by a full rank integer matrix A with the vector (1,1,...,1) in its row space, the package computes the degree and codimension of the dual (i.e. the A-discriminant variety), the Euclidean distance degree of X_A, the polar degrees of X_A, and the Chern-Mather class of X_A. Note that we do not require that X_A is normal. This package uses the algorithms described in [1] and [2]. For definitions of the objects computed by the package see [1,2].

References: \break [1] Martin Helmer and Bernd Sturmfels. "Nearest points on toric varieties." Mathematica Scandinavica 122, no. 2 (2018): 213-238. Arxiv version: https://arxiv.org/abs/1603.06544.\break [2] Martin Helmer and Bernt Ivar Utstol Nodland. "Polar degrees and closest points in codimension two." Journal of Algebra and Its Applications (2017): 1950095. Arxiv version: https://arxiv.org/abs/1711.02381.

## Version

This documentation describes version 3.01 of ToricInvariants.

## Source code

The source code from which this documentation is derived is in the file ToricInvariants.m2.

## Exports

• Functions and commands
• cmClass -- Computes the Chern-Mather class of a projective toric variety
• cmVolumes -- Computes the Chern-Mather volumes of a projective toric variety
• dualDegCodim -- Computes the degree and codimension of the dual to a projective toric variety
• edDeg -- Computes the (generic) Euclidean distance degree of a projective toric variety
• polarDegrees -- Computes the polar degrees of a projective toric variety
• Methods
• "cmClass(Matrix)" -- see cmClass -- Computes the Chern-Mather class of a projective toric variety
• "cmVolumes(Matrix)" -- see cmVolumes -- Computes the Chern-Mather volumes of a projective toric variety
• "dualDegCodim(Matrix)" -- see dualDegCodim -- Computes the degree and codimension of the dual to a projective toric variety
• "edDeg(Matrix)" -- see edDeg -- Computes the (generic) Euclidean distance degree of a projective toric variety
• "polarDegrees(Matrix)" -- see polarDegrees -- Computes the polar degrees of a projective toric variety
• Symbols
• ForceAmat (missing documentation)
• Output (missing documentation)
• TextOutput (missing documentation)

## For the programmer

The object ToricInvariants is .